Related papers: Resolvent-Techniques For Multiple Exercise Problem…
We study solutions to nonlinear hyperbolic systems with fully nonlinear relaxation terms in the limit of, both, infinitely stiff relaxation and arbitrary late time. In this limit, the dynamics is governed by effective systems of parabolic…
We propose a comprehensive framework for policy gradient methods tailored to continuous time reinforcement learning. This is based on the connection between stochastic control problems and randomised problems, enabling applications across…
In this article, we study the classical finite-horizon optimal stopping problem for multidimensional diffusions through an approach that differs from what is typically found in the literature. More specifically, we first prove a key…
This paper studies the optimal multiple-stopping problem arising in the context of the timing option to withdraw from a project in stages. The profits are driven by a general spectrally negative Levy process. This allows the model to…
This work presents a multiscale framework to solve an inverse reinforcement learning (IRL) problem for continuous-time/state stochastic systems. We take advantage of a diffusion wavelet representation of the associated Markov chain to…
In this paper we consider discrete and continuous time risk sensitive optimal stopping problem. Using suitable properties of the underlying Feller-Markov process we prove continuity of the optimal stopping value function and provide formula…
In this paper, we study an optimal stopping problem in the presence of model uncertainty and regime switching. The max-min formulation for robust control and the dynamic programming approach are adopted to establish a general theoretical…
We study the setting of \emph{performative reinforcement learning} where the deployed policy affects both the reward, and the transition of the underlying Markov decision process. Prior work~\parencite{MTR23} has addressed this problem…
We consider the multi-refraction strategies in two equivalent versions of the optimal dividend problem in the dual (spectrally positive L\'evy) model. The first problem is a variant of the bail-out case where both dividend payments and…
A direct numerical solution of the radiative transfer equation or any kinetic equation is typically expensive, since the radiative intensity depends on time, space and direction. An expansion in the direction variables yields an equivalent…
We study optimal stopping for diffusion processes with unknown model primitives within the continuous-time reinforcement learning (RL) framework developed by Wang et al. (2020), and present applications to option pricing and portfolio…
In a classical optimal stopping problem the aim is to maximize the expected value of a functional of a diffusion evaluated at a stopping time. This note considers optimal stopping problems beyond this paradigm. We study problems in which…
This paper presents a novel deep learning framework for solving multiple optimal stopping problems in high dimensions. While deep learning has recently shown promise for single stopping problems, the multiple exercise case involves complex…
Resolvent analysis is a powerful tool that can reveal the linear amplification mechanisms between the forcing inputs and the response outputs about a base flow. These mechanisms can be revealed in terms of a pair of forcing and response…
In this paper, we consider multistopping problems for finite discrete time sequences $X_1,...,X_n$. $m$-stops are allowed and the aim is to maximize the expected value of the best of these $m$ stops. The random variables are neither assumed…
In Monte-Carlo methods the Markov processes used to sample a given target distribution usually satisfy detailed balance, i.e. they are time-reversible. However, relatively recent results have demonstrated that appropriate reversible and…
This paper studies the bail-out optimal dividend problem with regime switching under the constraint that the cumulative dividend strategy is absolutely continuous. We confirm the optimality of the regime-modulated refraction-reflection…
We establish a systematic solution method for optimal stopping problems of spectrally negative L\'evy processes. Our approach relies essentially on the potential theory, in particular the Riesz decomposition and the maximum principle. Using…
This paper considers an optimal impulse control problem of dynamical systems generated by a flow. The performance criteria are total costs over the infinite time horizon. Apart from the main performance to be minimized, there are multiple…
Markov-modulated L\'evy processes with two different regimes of restarting are studied. These regimes correspond to the completely renewed process and to the process of Markov modulation, accompanied by jumps. We give explicit expressions…