arXiv subjects

Ihsan Arharas

Publications and source records attributed to Ihsan Arharas.

4 recordsLinked to original sources

arXiv2026

Deep Learning for Energy Market Contracts: Dynkin Game with Doubly RBSDEs

We formulate a Contract for Difference (CfD) with early exit options as a two-player zero-sum Dynkin game, reflecting the strategic interaction between an electricity producer and a regulatory entity. The game incorporates penalties for early termination and mean-reverting price dynamics, with the value characterized through a doubly reflected backward stochastic differential equation (DRBSDE). To compute the contract value and optimal stopping strategies, we develop a neural solver that approximates the DRBSDE solution using a sequence of neural networks trained on simulated trajectories. The method avoids discretizing the state space, supports time-dependent barriers, and scales to high-dimensional settings. We establish a convergence result and test the method on two scenarios: a benchmark symmetric game in 20 dimensions, and a CfD model with 24-dimensional electricity prices representing multiple European zones. The results demonstrate that the proposed solver accurately captures the contract's value and optimal stopping regions, with consistent performance across dimensional settings.

math.OC↗

arXiv2024

Optimal Stopping Under Model Uncertainty in a General Setting

We consider the optimal stopping time problem under model uncertainty $R(v)= {\text{ess}\sup\limits}_{ \mathbb{P} \in \mathcal{P}} {\text{ess}\sup\limits}_{τ\in \mathcal{S}_v} E^\mathbb{P}[Y(τ) \vert \mathcal{F}_v]$, for every stopping time $v$, set in the framework of families of random variables indexed by stopping times. This setting is more general than the classical setup of stochastic processes, and particularly allows for general payoff processes that are not necessarily right-continuous. Under weaker integrability, and regularity assumptions on the reward family $Y=(Y(v), v\in \mathcal{S})$, we show the existence of an optimal stopping time. We then proceed to find sufficient conditions for the existence of an optimal model. For this purpose, we present a universal Doob-Meyer-Mertens's decomposition for the Snell envelope family associated with $Y$ in the sense that it holds simultaneously for all $\mathbb{P} \in \mathcal{P}$. This decomposition is then employed to prove the existence of an optimal probability model and study its properties.

math.PR↗

arXiv2023

Doubly Reflected BSDEs in the predictable setting

In this paper, we introduce a specific kind of doubly reflected Backward Stochastic Differential Equations (in short DRBSDEs), defined on probability spaces equipped with general filtration that is essentially non quasi-left continuous, where the barriers are assumed to be predictable processes. We call these equations predictable DRBSDEs. Under a general type of Mokobodzki's condition, we show the existence of the solution (in consideration of the driver's nature) through a Picard iteration method and a Banach fixed point theorem. By using an appropriate generalization of Itô's formula due to Gal'chouk and Lenglart, we provide a suitable a priori estimates which immediately implies the uniqueness of the solution.

math.PR↗

arXiv2023

Reflected and Doubly RBSDEs with Irregular Obstacles and a Large Set of Stopping Strategies

We introduce a new formulation of reflected BSDEs and doubly reflected BSDEs associated with irregular obstacles. In the first part of the paper, we consider an extension of the classical optimal stopping problem over a larger set of stopping systems than the set of stopping times (namely, the set of split stopping times), where the payoff process $ξ$ is irregular and in the case of a general filtration. Split stopping times are a powerful tool for modeling financial contracts and derivatives that depend on multiple conditions or triggers, and for incorporating stochastic processes with jumps and other types of discontinuities. We show that the value family can be aggregated by an optional process $v$, which is characterized as the Snell envelope of the reward process $ξ$ over split stopping times. Using this, we prove the existence and uniqueness of a solution $Y$ to irregular reflected BSDEs. In the second part of the paper, motivated by the classical Dynkin game with completely irregular rewards considered by Grigorova et al. (2018), we generalize the previous equations to the case of two reflecting barrier processes.

math.PR↗