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Nizar Touzi
(New York University, Tandon School of Engineering)
Title: Model risk hedging through Distributionally Robust Sensitivity
Abstract: Distributionally robust optimization studies the worst deviation of an evaluation functional on the Wasserstein ball centered at the model of interest. We derive explicit sensitivity analysis under marginal and martingale constraints which provide first order semi-static hedge against model risk.
Kais Hamza
(Monash University)
Title: Alternative models in Finance - Mimicking
Abstract: Motivated by questions in finance, we are interested in constructing new processes that emulate existing ones by preserving finance-relevant characteristics, such as marginal distributions and the martingale property. We refer to this approach as mimicking. This could enable the development of alternative models for asset pricing, with the aim of improving upon existing models while retaining (European) option prices.
Marwa Khalil
(Tunis El Manar University, National Engineering School of Tunis)
Title: On the dynamics of waves driven by additive Fractional noise : a Malliavin calculus approach.
Abstract: This presentation focuses on the analysis of the properties of the solution to the wave equation perturbed by an additive fractional noise, with an emphasis on statistical applications. More precisely, the aim is to examine the covariance structure of this spatio-temporal solution in order to better understand its probabilistic behavior. To this end, classical techniques from Malliavin calculus are employed, a powerful tool in stochastic analysis for investigating the regularity and fine properties of random processes. The study of the covariance plays a central role in estimating the Hurst parameter H, which characterizes both the long range dependence and the regularity of the fractional noise. The proposed approach seeks to construct an estimator of H that is both consistent and asymptotically normal. This investigation thus contributes to a deeper understanding of the behavior of dynamical systems influenced by fractional noise and paves the way for various applications in stochastic modeling.
Olfa Draouil
(Tunis El Manar University, Faculté des Sciences de Tunis)
Title: White noise calculus for time changed Brownian motion
Abstract: In this work, we propose a framework of white noise calculus to work with time changed Brownian motion. For this, we work with different information flows which may include or not knowledge of the time change process. In this setting we show that the time changed Brownian motion is a martingale, which has no independent increments in general. We study chaos expansions and define three different stochastic derivative operators including the Hida-Malliavin derivative. We show that these operators coincide and hence we obtain three different representations of the stochastic derivative. Finally, we obtain the Clark-Ocone formula with respect to the time-changed Brownian motion.
Rafik Amor Aguech
Rafik Amor Aguech
(King Saud University)
Title: On a class of unbalanced step-reinforced random walks
Abstract: A step-reinforced random walk is a discrete-time stochastic process with long-range dependence. At each step, with a fixed probability α , the so-called positively step-reinforced random walk repeats one of its previous steps, chosen randomly and uniformly from its entire history. Alternatively, with probability 1-α , it makes an independent move.
For the so-called negatively step-reinforced random walk, the process is similar, but any repeated step is taken with its direction reversed.
These random walks have been introduced respectively by Simon (1955) and Bertoin (2024) and are sometimes referred to the self confident step-reinforced random walk and the counterbalanced step-reinforced random walk respectively. In this talk, we introduce a new class of unbalanced step-reinforced random walks for which we prove the strong law of large numbers and the central limit theorem. In particular, our work provides a unified treatment of the famous elephant random walk introduced by Schutz and Trimper (2004) and the positively and negatively step-reinforced random walks.
Asma Khedher
(University of Amsterdam)
Title: Measure-valued CARMA processes
Abstract: In this paper, we examine continuous-time autoregressive moving-average (CARMA) processes on Banach spaces driven by Lévy subordinators. We show their existence and cone-invariance, investigate their first and second order moment structure, and derive explicit conditions for their stationarity. Specifically, we define a measure-valued CARMA process as the analytically weak solution of a linear state-space model in the Banach space of finite signed measures. By selecting suitable input, transition, and output operators in the linear state-space model, we show that the resulting solution possesses CARMA dynamics remain in the cone of positive measures defined on some spatial domain. We also illustrate how positive measure-valued CARMA processes can be used to model the dynamics of functionals of spatio- temporal random fields and connect our framework to existing CARMA-type models from the literature, highlighting its flexibility and broader applicability.
Yadh Hafsi
(Université Paris-Saclay)
Title: Optimal Execution under Incomplete Information
Abstract: We study optimal liquidation strategies under partial information for a single asset within a finite time horizon. We propose a model tailored for high-frequency trading, capturing price formation driven solely by order flow through mutually stimulating marked Hawkes processes. The model assumes a limit order book framework, accounting for both permanent price impact and transient market impact. Importantly, we incorporate liquidity as a hidden Markov process, influencing the intensities of the point processes governing bid and ask prices. Within this setting, we formulate the optimal liquidation problem as an impulse control problem. We elucidate the dynamics of the hidden Markov chain's filter and determine the related normalized filtering equations. We then express the value function as the limit of a sequence of auxiliary continuous functions, defined recursively. This characterization enables the use of a dynamic programming principle for optimal stopping problems and the determination of an optimal strategy. It also facilitates the development of an implementable algorithm to approximate the original liquidation problem. We enrich our analysis with numerical results and visualizations of candidate optimal strategies.
Ibtissam Hdhiri
(University of Gabes, Faculty of Sciences of Gabes)
Title: On Some Non-Markovian Classes of Stochastic Impulse Control Problems
Abstract: Stochastic impulse control provides a powerful framework for modeling discrete, costly interventions in uncertain systems. In this talk, we investigate several classes of stochastic impulse control problems in non-Markovian settings. We focus on three interconnected frameworks: the risk-neutral formulation, the risk-sensitive case, and systems with execution delay.
Our approach relies on probabilistic tools such as reflected backward stochastic differential equations (RBSDEs), Snell envelopes, and generalized optimal stopping techniques.
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