arXiv subjects

Ibtissam Hdhiri

Publications and source records attributed to Ibtissam Hdhiri.

3 recordsLinked to original sources

arXiv2026

Doubly reflected BSDEs driven by Inhomogeneous simple Levy processes: Applications to generalized Dynkin games

We study doubly reflected backward stochastic differential equations with jumps and two completely separated right-continuous with left limits barriers in a filtration generated by an inhomogeneous Levy process. We establish existence and uniqueness results under a stochastic Lipschitz condition on the driver by means of a penalization method. We also prove a comparison principle and present two closely related applications. The first concerns the nonlinear valuation of an American game option in such a Levy market, while the second addresses the associated generalized Dynkin game under nonlinear expectation. Moreover, under suitable semicontinuity assumptions on the barriers, we establish the existence of a saddle point for the game.

math.PR↗

arXiv2026

Optimal stochastic impulse control problem with delay with actions decided at the execution time

In this paper, we consider a class of stochastic impulse control problem when there is a fixed delay $Δ$ between the decision and execution times. The dynamics of the controlled system between two impulses is an arbitrary adapted stochastic process. Unlike the most existing literature, we consider the problem when the impulse sizes are decided at the execution time in both risk-neutral and risk-sensitive cases. This model fits more, in the real life, for some problems such as the pricing of swing options. The horizon T of the problem can be finite or infinite. In each case we show the existence of an optimal strategy. The main tools we use are the notions of reflected Backward Stochastic Differential Equations (BSDEs for short) and the Snell envelope of processes.

math.PR↗

arXiv2008

Stochastic Impulse Control of Non-Markovian Processes

We consider a class of stochastic impulse control problems of general stochastic processes i.e. not necessarily Markovian. Under fairly general conditions we establish existence of an optimal impulse control. We also prove existence of combined optimal stochastic and impulse control of a fairly general class of diffusions with random coefficients. Unlike, in the Markovian framework, we cannot apply quasi-variational inequalities techniques. We rather derive the main results using techniques involving reflected BSDEs and the Snell envelope.

math.PR↗