14–18 September 2026 · CIRM, Marseille, France
Interactions in applied mathematics for economics, finance and insurance
Monday 14 September
Chairwoman: Amal Omrani
09:00–09:15
Opening welcome speech
Emmanuel Lepinette, Mohamed Amine BEN AMOR and Amal Omrani.
09:20–10:00
Emmanuel Lepinette
Paris-Dauphine PSL University, France.
Fundamental concepts in financial mathematics: from traditional approaches to recent advances.
10:05–10:20
Coffee Break
10:25–11:25
Mathieu Rosembaum
Paris-Dauphine PSL University, France.
A unified theory of order flow, market impact and volatility.
Abstract
We propose a microstructural model for the order flow in financial markets that distinguishes between core orders and reaction flow, both modeled as Hawkes processes. This model has a natural scaling limit that reconciles a number of salient empirical properties: persistent signed order flow, rough trading volume and volatility, and power-law market impact. In our framework, all these quantities are pinned down by a single statistic H0 , which measures the persistence of the core flow. Specifically, the signed flow converges to the sum of a fractional process with Hurst index H0 and a martingale, while the limiting traded volume is a rough process with Hurst index H0 − 1/2. No-arbitrage constraints imply that volatility is rough, with Hurst parameter 2H0 − 3/2, and that the price impact of trades follows a power law with exponent 2 − 2H0 . The analysis of signed order flow data yields an estimate H0 close to 3/4. This is not only consistent with the square-root law of market impact, but also turns out to match estimates for the roughness of traded volumes and volatilities remarkably well.
11:35–12:10
Vladimir Troitsky
University of Alberta, Edmonton, Canada.
Linear operators: continuity vs boundedness.
Abstract
It is a standard fact that a linear operator between normed spaces is bounded if and only if it is continuous. This fact, and many other facts, are special cases of a general principle that a linear operator is continuous (in a certain sense) if and only if it is bounded (again, in a certain sense). To formulate this principle, we will use convergence structures to define a continuous operator; we will use bornologies to define bounded operators. We will discuss several applications to vector and Banach lattices.
12:30–13:30
Lunch
Chairwoman: Dorsaf Cherif
14:00–14:40
Yuri Kabanov
Université Marie et Louis Pasteur, Besançon, France, and Lomonosov MSU, Russia.
On exit probabilities for generalized Ornstein–Uhlenbeck processes.
Abstract
Nowadays, insurance companies place their capital reserves in stock markets to obtain additional gain. The collective risk theory assuming absence of risky investment became obsolete. To replace it, a new theory emerged. In 1993 J. Paulsen suggested to describe the reserve evolution by a generalized Ornstein–Uhlenbeck process and the development was con- centrated around this modeL The problem is how to explain the results to master students: the existing studies are based on advanced mathematical tools and cumbersome estimates. In the recent notes [1], [2] it was devel- oped a new approach how to get and solve IDE for the ruin probabilities and obtain their asymptotic behavior in the case where risky asset follows gBm and the business process has one-sided jumps (downward for the non-life insurance and upward for the annuity payments. The approach is based on the analysis of IDE and a verification theorem identifying its solution with the ruin probability as a function of the initial capital. In the current study it was extended a still special case of the OU process where the business process is a Lévy process of bounded variation with one-side jumps.
14:50–15:20
Benrjab Asma
Tunis El Manar University, Tunis, Tunisia.
Order properties of Free Banach Lattices.
Abstract
Free Banach lattices allow us to construct a Banach lattice from a set, a Banach space, or a lattice, through suitable extension properties.In this talk, we first introduce these constructions and their universal prop- erties. We then study order properties of free Banach lattices, focusing on the strong Nakano property and its behavior for free Banach lattices generated by Banach spaces. Finally, we turn to the free Banach lattice F BL⟨L⟩ generated by a lattice L. Several properties of this construction have already been studied; we continue this investigation by studying fur- ther structural properties, including strong units, density character,order density, projection bands and quasi-interior points.
15:30–16:00
Eugene Bilokopytov
ICMAT (Instituto de Ciencias Matemáticas), Madrid, Spain.
Semicontinuity properties of Banach lattices.
Abstract
We consider various properties of a normed lattice, which are simi- lar to the order semicontinuity (a.k.a.) the Fatou property. In particu- lar, a normed lattice F is order continuous iff every renorming of F is semicontinuous. A normed lattice embeds as a regular sublattice of a monotonically complete Banach lattice iff it is weakly Fatou. While the classical Kakutani theorem states that AM-spaces are precisely the closed sublattices of C (K)-spaces, we show that the semicontinuous AM-spaces are precisely the closed regular sublattices of C (K)-spaces. Finally, we prove that for a normed space E, the AM-space of positively homoge- neous weak* continuous functions on BE ∗ has the Fatou property iff it is a regular sublattice of C (BE ∗ , w∗ ) iff dim E < ∞.
16:05–16:20
Coffee Break
16:25–17:10
Anke Kalauch
Faculty of Mathematics, TU Dresden, Germany.
Pre-Riesz Spaces: what we know, what we don’t know.
Abstract
Pre-Riesz spaces were invented in 1993 in Nijmegen as those ordered vector spaces that can be order densely embedded into Riesz spaces. A next wave of investigation started in 2006, when substructures of pre-Riesz spaces were studied systematically. In recent years, interest has grown toward structure-preserving operators in pre-Riesz spaces, applications and links to other fields of functional analysis. Since the Dutch-German collaboration on pre-Riesz spaces reaches the age of 20, the time seems right to evaluate the degree of maturity of the project. We survey some achievements and related problems that remained either unsolved or even untouched so far. For instance, we discuss bands and orthomorphisms, disjointness-preserving operators and C0-semigroups, and Ogasawara-type theorems, where the Riesz space theory is well understood but the pre-Riesz space theory needs broader care in its coming of age.
17:20–17:50
Janko Stennder
TU Dresden University, Dresden, Germany.
A Nakano-type theorem in pervasive pre-Riesz spaces.
Abstract
The classical Nakano theorem characterizes the disjointness of order continuous functionals on Archimedean vector lattices in terms of their null ideals and carriers. We introduce generalizations of the notions of null ideal and carrier to ordered vector spaces and show that, on pervasive pre-Riesz spaces, the same characterization as in Nakano’s theorem holds for positive order continuous functionals. These results contribute to the recent developments in the theory of disjointness of operators beyond the setting of vector lattices, which we will briefly review before presenting the main results.
18:00–18:30
Timur Oikhberg
University of Illinois at Urbana-Champaign, USA.
Free Banach lattices and associated function spaces.
Abstract
It is well known that a free Banach lattice (in this talk, the free p- convex lattice F BL(p)[E] over a Banach space E) can be represented as a space of functions on E, and this gives rise to several related function spaces. We examine properties of “natural” embeddings between these spaces, as well their “order” (Fatou-like) properties, which turn out to be related to the geometry of the underlying Banach space E.
19:30–20:30
Dinner
Tuesday 15 September
Chairwoman: Laurence Carassus
09:00–09:40
Pedro Tradacete
instituto de Ciencias Matemáticas – CSIC, Spain.
Recent progress in Banach lattices.
Abstract
We will survey recent results in the theory of Banach lattices, focusing mainly on the interactions with Banach space theory and descriptive set theory.
09:50–10:20
Gonzalo Martínez Fernández
UCM University, Madrid, Spain.
Abstract
We introduce free products, that is, coproducts, in the category of Banach lattices and contractive lattice homomorphisms. We give a concrete construction of the free product of an arbitrary family of Banach lattices as a quotient of a free Banach lattice. For compact Hausdorff spaces K1 and K2 we identify C(K1)∗C(K2) lattice isomorphically with C(K1 ∗ K2), where K1 ∗ K2 denotes the join of topological spaces. We further discuss free factors of free Banach lattices, and exploit the existence of non-trivial homology spheres to show that a free Banach lattice can have free factors which are not isomorphic to free Banach lattices. This is joint work with Pedro Tradacete Pérez.
Free products of Banach lattices.
10:25–10:40
Coffee Break
10:45–11:25
Crista Cuchiero
University of Vienna, Austria.
Dynamic universal approximation and optimal control for path-dependent systems via signature SDEs.
Abstract
Many applications in generative time series modeling, particularly in finance, require stochastic dynamics that are genuinely path-dependent and non-Markovian. From a numerical perspective, the most natural route is to lift path dependence to an enlarged state space, thereby obtaining a Markovian approximation of the original dynamics. Among such lifts, signature SDEs provide a canonical and model-agnostic choice, building on the strong algebraic and approximation-theoretic properties of path signatures, which form a universal and non-parametric feature set for paths. We explain how this leads to dynamic universal approximation results for generic non-Markovian SDEs. We also show how the resulting finite-dimensional signature SDEs can be used in optimal control problems with path-dependent dynamics and objectives, reducing, for instance, the infinite-dimensional Hamilton-Jacobi-Bellman PDE to a computationally much simpler Riccati ODE.
11:35–12:15
Johannes Langner
MICS, CentraleSupélec, Université Paris-Saclay, France.
P-Sensitive Functions and Localizations.
Abstract
This paper assumes a robust stochastic model where a set P of proba- bility measures replaces the single probability measure of dominated mod- els. We introduce and study P-sensitive functions defined on robust func- tion spaces of random variables. We show that P-sensitive functions are precisely those that admit a representation via so-called functional local- ization. The theory is applied to solving robust optimization problems, to convex risk measures, and to the study of no arbitrage in robust one- period financial models. Keywords: robustness, non-dominated set of probabilities, P-sensitivity, functional localization, convex risk measures, superhedging functional
12:30–13:30
Lunch
Chairwoman: Emma Hubert
14:00–14:40
Luciano Campi
University of Milan, Italy.
Optimal Mean Field CCEs;Optimal Coarse Correlated Equilibria in Mean Field Games: Linear Programming and No-Regret Learning.
Abstract
We introduce optimal coarse correlated equilibria for continuous-time mean field games. A coarse correlated equilibrium is a randomized rec- ommendation scheme from which no player can gain by ignoring the rec- ommendation and switching to an alternative strategy. The problem is as follows: a moderator selects, among all mean-field coarse correlated equilibria, one that optimizes a prescribed performance criterion, which may differ from the representative player’s objective. After formulating the problem, we develop a linear programming (LP) formulation, prove the existence of optimal LP coarse correlated equilibria, and relate the LP characterization to the original probabilistic setting. Building on this characterization, we design a no-regret primal-dual algorithm, based on an equivalent Lagrangian formulation of the external-regret constraint, for learning such equilibria. We provide explicit convergence rates for the learning algorithm, and numerical examples illustrate the method. This talk is based on a joint paper with F. Cannerozzi and I. Tzouanas (Biele- feld University).
14:50–15:20
Amal Omrani
Paris-Dauphine PSL University, France.
Explicit Characterization and Backward Construction of Superhedging Prices with Transaction Costs.
Abstract
Under proportional transaction costs, the super-hedging price is classi- cally a supremum over consistent price systems — complete in theory, but rarely computable. We make it explicit in discrete time by replacing the conditional law of returns with their conditional support: the worst-case constraint reduces to a supremum over a calibrated return band, attained by convexity at its two endpoints. This yields a closed-form one-step price — the larger of a pure-price bound and a strategy-driven bound — and the exact interval of feasible strategies. On a payoff class stable under this step (and capturing the inventory dependence frictions induce), a single backward recursion reconstructs prices and hedges, finite precisely under Absence of Immediate Profit. Illustrated out-of-sample on SPY.
15:30–16:00
Ahsen Sena Yurtoğlu
Bursa Technical University, Department of Mathematics, Bursa, Turkey.
Abstract
In this work, we study quasi KB operators and their demi versions on locally solid vector lattices. We investigate the fundamental properties of quasi KB operators and extend the analysis to the more general setting of locally solid vector lattices. In particular, the demi versions of quasi KB operators on Banach lattices are extended to locally solid vector lattices through the notion of demi quasi KB operators. We examine their basic properties and investigate their relationship with quasi KB operators. Furthermore, we define the notions of p-quasi KB and p-demi quasi KB operators on lattice-normed vector lattices and study some of their fundamental properties. These results provide a broader framework for understanding quasi KB-type operators and their demi versions in different lattice structures.
Quasi KB Operators and Their Demi Versions.
16:05–16:20
Coffee Break
16:25–16:55
Samuel Tiersma
Leiden University, Netherlands.
A generalization of Kadison’s antilattice theorem.
Abstract
An ordered vector space is called an anti-lattice if no pair of incompa- rable elements has an infimum. This concept was introduced by Kadison, who proved that for von Neumann algebras, the anti-lattices are precisely the factors. Archbold showed that a C*-algebra is an anti-lattice if and only if it is prime. This talk, based on a joint work with Mark Roelands, features a computation-free proof of Archbold’s result which leverages the theory of pre-Riesz spaces, and generalizes it in several directions. First, the result is extended to JB-algebras, which generalize the self- adjoint part of a C*-algebra. Second, the anti-lattice property is strength- ened to finite sets of more than two elements: a finite subset of a prime JB-algebra has an infimum only if it has a least element. Finally, using the notion of disjointness and bands in pre-Riesz spaces introduced by Kalauch and van Gaans, we establish that disjointness in a JB-algebra is governed by its spectrum. Consequently, the poset of bands in a JB- algebra is isomorphic to the Boolean algebra of regular closed subsets of its spectrum, generalizing a well-known result for C(K)-spaces.
17:00–17:30
Sezer Bolat
Hacettepe University, Department of Mathematics, Ankara, Turkey.
Extending the (bo)-Fragment Theory to the Complex Setting.
Abstract
The complexification of vector lattices is a well-established and fun- damental concept in the theory of Riesz spaces [1]. Recently, the study of complexification has been extended to the framework of fragments and lateral orders in complex vector lattices [2]. Motivated by these devel- opments, the aim of this work is to investigate the complexification of lattice-normed vector lattices (LNVLs) and develop the associated frag- ment and lateral order structures within this new setting. We introduce the concept of complex (bo)-fragments, building upon the real (bo)-fragment theory recently developed in [3]. Our main results establishes that the complexification of an LNVL preserves decompos- ability if and only if the original space is decomposable. Furthermore, we establish that the Boolean algebra of fragments of a complex element is isomorphic to the Boolean algebra of fragments of its modulus. As a central result, we prove that the collection of complex (bo)-fragments of a given element inherently forms a Boolean algebra, demonstrating com- plete structural consistency with the real case. The results presented in this paper are founded on the work in [4]. Keywords: Complex lattice-normed vector lattice, (bo)-fragment, Boolean algebra, Lateral order, Decomposability.
17:40–18:10
Hamza Hafsi
University of Tunis, Tunisia.
Transfer Results for AL-, AM-, and KB-Properties in Truncated Normed Riesz Spaces.
Abstract
In this talk, we continue the study of the transfer of structural proper- ties between a truncated Riesz space E and its canonical unitization E⊕R. While previous work focuses on order-theoretic and completeness proper- ties, the present contribution investigates the transfer of three fundamen- tal norm properties of Banach lattices: the AL, AM, and Kantorovich– Banach (KB) properties. We establish characterizations of these properties in the unitization setting and describe the possible lattice norm extensions from E to E ⊕ R. In particular, we show that AL- and AM-norm extensions are character- ized by two natural one-parameter families of lattice norms. The non- unital case, as well as the transfer of the KB property, is also investigated. Several examples are provided to illustrate the results and their limita- tions.
18:20–18:50
Elroy Zeekoei
North-West University, South Africa.
On weak p – consistence.
Abstract
n n It is not always true that if xn −→ 0 weakly, then |xn | −→ 0 weakly, ∞ ∞ that is, in general, the lattice operations are not necessarily weakly se- quentially continuous. We show that if the elements of a sequence (xi ) in a Banach lattice E are pairwise disjoint, then (xi ) ∈ ℓweak p (E) ⇐⇒ (|xi |) ∈ ℓweak p (E).
19:30–20:30
Dinner
Wednesday 16 September
Chairman: Emmanuel Lepinette
09:00–09:30
Youssef Azouzi
Tunis El Manar University.
On Komlós’ Theorem in Banach lattices, part 1.
Abstract
In this talk, I present several results related to the celebrated theorem of Komlós, which states that every bounded sequence in L1(P) admits a subsequence such that the Cesàro means of every further subsequence converge almost surely to the same limit. We begin by reviewing the classical theorem, together with some of its variants and extensions in the literature, and discuss several different approaches to its proof. We seek to identify the “best” proof. In particular, we point out that some proofs in the literature contain significant gaps. Recently, an important extension of Komlós’ theorem has been developed in a measure-free setting, benefiting from the generalization of almost-everywhere convergence to unbounded order convergence in vector lattices. In the second part, we explain the advantages of this generalization, due essentially to Gao, Xanthos, and Troitsky, and present new results in this direction. In particular, we answer several open questions raised by these authors. In our approach to answering one of these questions, we strengthen a result of Erdős and Magidor and show that it can be formulated in a much more general setting. The talk is based on joint work with Wassim Dhifaoui, who will present the second part of the project, which addresses an important open question concerning the converse of Komlós’ theorem. The result holds in a remarkably general setting, and its elegant proof highlights the power of the machinery developed in the abstract theory of Banach lattices.
09:40–10:10
Wassim Dhifaoui
Tunis El Manar University.
On Komlós Theorem in Banach lattices, part 2.
Abstract
This talk is a continuation of Youssef Azouzi’s talk. We first study Komlós sets in Banach lattices and investigate their structural properties. Moreover, we answer affirmatively a question posed by Gao, Troitsky, and Xanthos, and provide a simplified proof of a result from [7]. We also develop a general construction method for producing Banach lattices with the Komlós property. Finally, we turn our attention to the Komlós and pre-Komlós properties in C(K). When K is a compact metric space, we provide full characterizations of these properties in terms of the topology of K, thereby identifying the precise topological conditions on K under which they hold. These results provide new structural insights into the interplay between Komlós-type properties and the underlying lattice structure.
10:15–10:30
Coffee Break
10:35–11:00
Michèle Vanmaele
Ghent University, Ghent, Belgium.
Abstract
We propose a numerical method for the valuation of European-style options under two-asset infinite-activity exponential Lévy models. Our method extends the effective approach developed by Wang, Wan and Forsyth for the 1-dimensional case to the 2-dimensional setting and is applicable for general Lévy measures under mild assumptions. A tailored discretization of the non-local integral term is developed, which can be efficiently evaluated by means of the fast Fourier transform. For the temporal discretization, the semi-Lagrangian θ-method is employed in a convenient splitting fashion, where the diffusion term is treated implicitly and the integral term is handled explicitly by a fixed-point iteration. Numerical experiments for put-on-the-average options under Normal Tempered Stable dynamics reveal a favourable convergence behaviour of our method whenever the exponential Lévy process has finite variation. In addition, a relevant theoretical convergence result for the discretization of the integral term is proved. This talk is based on joint work with Massimiliano Moda (University of Antwerp, Belgium), Karel in ’t Hout (University of Antwerp, Belgium) and Fred Espen Benth (BI Norwegian Business School, Oslo, Norway). Based on the paper: M. Moda, K. J. in ’t Hout, M. Vanmaele and F. E. Benth, “Numerical Valuation of European Options under Two-Asset Infinite-Activity Exponential Lévy Models”, Applied Mathematical Finance, 2026, to appear, DOI: 10.1080/1350486X.2026.2715128.
Numerical Valuation of European Options under Two-Asset Infinite-Activity Exponential Lévy Models.
11:10–11:50
Tahir Choulli
University of Alberta, Edmonton, Canada.
Novel Esscher Concepts for various Risks in Finance and Insurance: Theory and empirical studies.
Abstract
Our principal leitmotif herein lies in pricing various claims within an informational setting that covers both life insurance and finance. This framework is represented by the triplet (S, F, τ ). Herein F is the “public” flow of information which is available overtime to all agents, S is the dis- counted price process of d-tradable assets, and τ is an arbitrary random time whose occurrence might not be observable via F. This framework covers the credit risk theory setting where τ represents the default time of a firm/client, the life insurance setting where τ models the death time of an insured, and other areas of finance to cite a few. For the resulting stopped model (S τ , G), where G is the flow that contains F and makes τ an observable random time when it occurs, we address the pricing prob- lem using Esscher concept. Given that τ brings various informational risks, certainly these risks cannot be priced by the classical Esscher pric- ing method even if τ is subject to assumptions such as immersion. Besides the informational risks generated by the randomness of τ , there are risks intrinsic to the stocks’ jumps caused by the shock of τ . Again, the clas- sical Esscher fails somehow to deal with these latter risks even without any information discrepancy at all. This led us to rethought radically the concept of Esscher pricing, and introduce the second-order Esscher pricing notion for general continuous-time models to deal with the risks coming from assets’ jumps. Then we introduce a novel Esscher notion to quantify the informational risks afterwards. The second-order Esscher extends the classical notion of Esscher that is used in finance and actuarial sciences. Besides this novel notion, our contributions herein is multifold. We char- acterize its second-order Esscher densities via pointwise equations using the statistical parametrization of the model under consideration. We show that the bounds of the Esscher stochastic pricing interval, ]]Y inf , Y up [[, are solutions to two constrained reflected linear backward stochastic differen- tial equations, or equivalently reflected BSDEs with singular non Lipschitz generator. Besides applying this second-order Esscher to risk management and show how the second order catch features that the classical Esscher fails to achieve, we show that the second-order allows us to quantify mar- kets’s fear/stress more accurately. Our informational Esscher pricing con- cept allows us to obtain explicit pricing formulas for several vulnerable complex claims, and quantify the prices for various informational risks. This talk is based on the following joint works with Alla Elazkany (University of Alberta) and/or Michele Vanmaele (Ghent University, Bel- gium): [1] Choulli/Elazkany (2026): Novel Esscher (2026): Novel Esscher for informational risk and valuation of vulnerable claims. Preprint. [2] Choulli/Elazkany/Vanmale (2025): The second-order Esscher with applications: Risk management and fear quantification. Preprint. [3] Choulli/Elazkany/Vanmale (2025): The second-order Esscher martingale densities for continuous-time market models: Frontiers of Mathematical Finance, Vol. 6, 2025, pp. 16-66.
12:00–13:00
Lunch
13:15
Departure for the excursion by bus
Thursday 17 September
Chairman: Mohamed Amine BEN AMOR
09:15–10:00
Paolo Guasoni
DCU University, Dublin, Ireland.
Holding Stocks, Trading Bonds.
Abstract
Why do rational investors actively trade long-term bonds? This paper solves a continuous-time exchange economy with heterogeneous CARA agents, common information, stochastic dividend growth, personal in- come, a stock, short-term lending, and long-term fixed-income securities. The economy is constructed to make trade difficult: in the constant- growth benchmark, heterogeneous agents do not rebalance after the initial allocation. With stochastic growth, however, shocks to expected divi- dends move interest rates and change the value of heterogeneous con- sumption plans and income hedges. In equilibrium agents hold stock positions that are constant after the initial allocation, while they trade long-term bonds dynamically. Bonds are the clean hedge because their deterministic coupons isolate discount-rate and growth-risk exposure from direct dividend cash-flow risk. The paper also develops an inaction-band implementation of frictionless bond targets, so that quadratic variation determines leading-order trading volume, and extends the mechanism to multiple stocks, multiple growth factors, and sinking funds.
10:10–10:25
Coffee Break
10:30–11:10
Emma Hubert
Paris-Dauphine University, Paris, France.
Revisiting contract theory with volatility control.
Abstract
In this talk, we revisit the resolution of continuous-time principal–agent problems with drift and volatility control, originally addressed by Cvi- tanić, Possamaı̈, and Touzi (2018) through dynamic programming and second-order backward stochastic differential equations(2BSDEs), and de- velop new results in this framework. We begin by introducing an alter- native problem in which the principal is allowed to directly control the quadratic variation of the output process. On the one hand, the resolution of this contractible-volatility problem follows the classical methodology of Sannikov (2008), thus relying on standard (first-order) BSDEs only. On the other hand, we introduce a new form of contracts allowing the princi- pal to achieve her contractible-volatility value, thereby ensuring both the optimality of this contract form and the equivalence between the original and the alternative problems. At the same time, this alternative approach reveals that the optimality of the contract form introduced by Cvitanić, Possamaı̈, and Touzi (2018) implicitly relies on an additional duality as- sumption, which was not identified before. This observation motivates the construction of new families of contracts that remain optimal even when the duality assumption fails. Altogether, this line of work both simplifies and strengthens the existing theory of continuous-time principal–agent problems with volatility control and opens new directions for further ex- tensions and applications in economics and finance. Talk based on joint works with Alessandro Chiusolo, Dylan Possamaı̈, and Nizar Touzi.
11:20–12:00
Duc Thinh Vu
Ghent University, Ghent, Belgium.
Optimal Additional Voluntary Contributions in the Presence of Jumps.
Abstract
Additional voluntary contributions (AVCs) have recently emerged as an important feature of pension fund design in the context of increasing life expectancy. Beyond mandatory employer contributions, pension plan members are encouraged to make additional contributions in order to secure adequate retirement income. In this research, we study an optimal AVC problem in a financial mar- ket subject to jumps. The model is formulated within a linear–quadratic stochastic control framework. Our main findings indicate that, when the wealth process is positive, the presence of jumps leads to more conservative investment behaviour compared to the no–jump case: pension members tend to allocate less wealth to the risky asset and increase their AVC rates. Moreover, in contrast to the diffusion-only setting, the jump model exhibits the feature that the dollar amount invested in the risky asset may become negative once wealth exceeds a certain threshold. This naturally motivates the consideration of trading constraints, in particular the no– short–selling constraint. We tackle the constrained problem by introducing an appropriate ansatz for the value function, which allows us to derive closed-form so- lutions for the optimal controls. The key tool is a verification argument based on viscosity solution theory. We provide several numerical examples to illustrate the results. This research is joint work with
12:30–13:30
Lunch
Chairwoman: Amal Omrani
14:00–14:35
Laurence Carassus
CentraleSupélec, Paris-Saclay University.
On the existence of personal equilibria in multistep incomplete financial markets.
Abstract
We consider an investor who, while maximizing his/her expected util- ity, also compares the outcome to a reference entity. A personal equi- librium is a strategy that is optimal when its own independent copy is used as the reference point. We show that, in a multistep, generically incomplete financial market model, such an equilibrium indeed exists, un- der appropriate technical assumptions. We also prove, for any exogenous reference point, existence and uniqueness of the corresponding optimal strategy; this exogenous-reference result is an independent ingredient of the analysis.
14:45–15:20
Mihail Zervos
LSE, London, England.
Long-run portfolio optimisation in the presence of proportional transaction costs: equivalent risk sensitive and robust formulations.
Abstract
We study long-run optimal investment with proportional transaction costs in a market comprising a money market account and a stock, under a no short-selling constraint. We consider two formulations: a risk sensi- tive portfolio optimisation problem, with risk sensitivity parameter θ, and a robust problem in which the investor penalises deviations from a refer- ence model by their relative entropy. We show that the two are associated with the same ergodic HJB equation, the robust problem corresponding to the risk sensitive one with θ replaced by −θ. After a suitable rescal- ing of the controls, both problems reduce to a one-dimensional singular stochastic control problem for the fraction of wealth invested in the stock. We derive the complete solution to this control problem by constructing a C 2 solution to its HJB equation. The solution takes three qualitatively different forms, depending on the position of the risk sensitive analogue of the Merton fraction relative to the interval ]0, 1[. In two of these, it is optimal for the investor to move the entire portfolio value into the money market account or into the stock at time 0 and make no trades thereafter. In the third one, it is optimal to keep the fraction of wealth invested in the stock inside an interval [α⋆ , β ⋆ ] ⊂ ]0, 1[ by exerting the minimal effort required to do so.
15:25–15:40
Coffee Break
15:45–16:15
Roman Drnovšek
Faculty of Mathematics and Physics, University of Ljubljana, Slovenia.
Positive Commutators on Banach lattices.
Abstract
We will present several results on positive commutators of positive operators on Banach lattices. We will start with the following finite- dimensional theorem. Let A and B be nonnegative matrices such that the commutator C = AB − BA is nonnegative as well. Then, up to similarity with a permutation matrix, C is a strictly upper triangular matrix, and so it is nilpotent. We will continue with the following infinite-dimensional analogue. Let A and B be bounded operators on a Banach lattice E such that the commutator C = AB − BA and the product BA are positive operators. If the product AB is a power-compact operator, then C is a quasi-nilpotent operator having a triangularizing chain of closed ideals of E. We will then consider the question which nonnegative matrices are commutators of nonnegative square-zero matrices. We will also treat infinite-dimensional analogues of these results.
16:25–16:55
David Muñoz Lahoz
ICMAT-UAM University, Madrid, Spain.
Wickstead’s conjecture on positive projections and non-representable Banach lattice algebras.
Abstract
Consider a projection matrix with nonnegative entries and constant diagonal entries, all equal to α. Wickstead showed that, in this setting, α can only be 0 or 1/n for some natural number n. He also conjectured that an analogous result should hold not only for projections on Rd , but also for positive projections P : X → X on an arbitrary Dedekind complete Banach lattice X. More precisely, he asked: if P can be written as P = α idX + T , with T disjoint from idX , which values can α take? This question arises in the broader context of Banach lattice algebras. One of the central problems in this area is the representation problem: whether every Banach lattice algebra can be faithfully represented as an algebra and a lattice of regular operators on some Dedekind complete vector lattice. Wickstead showed that, if α above did not take all values in [0, 1/2], then there existed Banach lattice algebras that are not unitarily representable. In this talk, we prove that Wickstead’s conjecture is true: α can only be 0 or 1/n for some natural number n. As a consequence, we obtain a negative answer to the representation problem: there exist Banach lattice algebras that are not representable, whether unital or not.
17:05–17:35
Ezgi Han Eryüksel Online talk
University of Ankara, Turkey.
Different Types of bo-Convergences in Lattice Scaled Spaces.
Abstract
Lattice scaled spaces (see [3]) generalize the notion of ultrametric spaces to the settings of Garrett Birkhoff’s lattice theory in such a way that most of the lattice theoretical notions can be studied in lattice scaled spaces. Following the approach of [3], we investigate how distinct lattice order convergences induce corresponding convergence structures on these spaces. Classical order convergence plays a central role in measure theory and various areas of analysis. Recently, in [1], various versions of order con- vergences and their applications were studied. The study focuses on clar- ifying the implications and structural differences between o1 -, o2 -, and o3 -convergences in the lattice setting. In the present talk, bo1 -, bo2 -, and bo3 -convergences in lattice scaled spaces will be introduced, and their properties will be investigated. We explore the relationships among these induced convergences, with special atten- tion given to their behavior with relative sublattices. Most of the prop- erties and equivalences are derived under the hypothesis of infinite dis- tributivity on the underlying lattice. The results presented in this talk are based on the joint work [2]. Keywords: Lattice scaled space, distributive lattice, order convergence, stability
19:30–20:30
Dinner
Friday 18 September
Chairman: Mohamed Amine BEN AMOR
09:00–09:40
Bruce Watson
Witz University, South of Africa.
Riesz spaces, stochastics and ergodic theory.
Abstract
This talk presents an overview of the evolution of stochastic and er- godic theory in Riesz spaces. It is a survey of the developments in the area over the past 25 years. Some of the measure theoretic origins and applications will also be covered.
09:50–10:20
Luan Naude
University of Pretoria, South of Africa.
Locally band preserving functions and Riemann integration
Abstract
Roelands and Schwanke recently developed a theory of differentiation on Φ-algebras in (1). We have shown that a super order differentiable function f defined on an order interval has the following property: when- ever P(x) = P(y) for x, y ∈ dom(f ) and a band projection P, we have that P(f (x)) = P(f (y)). Functions with this property are called locally band preserving, and we study this property to continue the work started in (1). We discuss how many classical results, such as the extreme value theorem and mean value theorem, can be recovered for these functions in Dedekind complete unital f -algebras and construct a Riemann integral for locally band preserving functions defined on an order interval. This talk is based on joint work with Eder Kikianty, Mark Roelands, and Christopher Schwanke.
10:25–10:40
Coffee Break
10:45–11:15
Kawtar Ramdane
Ibn Tofail University, Moroco.
Concentration Inequalities in Riesz Spaces.
Abstract
We develop measure-free analogues of the Efron–Stein and Hoeffding– Azuma inequalities in Riesz spaces. Using conditional expectation op- erators, we formulate notions of conditional variance and independence adapted to ordered structures, and derive bounds for the fluctuations of Riesz-space-valued random variables. This provides a unified framework for concentration phenomena without relying on an underlying probabil- ity measure.
11:25–12:00
Florian Boisen
TU Dresden University, Dresden, Germany.
Finitely additive measures and the T-strong dual of L∞(T).
Abstract
The norm dual of the space L∞(P) for a probability space (Ω, A, P) can be described as the space of all finitely additive measures on A that are absolutely continuous with respect to P. In this talk, we give a similar representation for the T-strong dual of L∞(T), where T is a conditional expectation operator on a Dedekind complete Riesz space. To this end, we introduce finitely additive measures on the set of all components of weak order units with values in the range of T and develop a corresponding integration theory. This talk is based on joint work with Anke Kalauch, Wen-Chi Kuo, Janko Stennder, and Bruce A. Watson.
12:00–12:15
Closing speech
12:30–13:30
Lunch
The End.