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We characterise the value function of the optimal dividend problem with a finite time horizon as the unique classical solution of a suitable Hamilton-Jacobi-Bellman equation. The optimal dividend strategy is realised by a Skorokhod…

Probability · Mathematics 2017-11-27 Tiziano De Angelis , Erik Ekström

We consider the diffusive limit of a typical pure-jump Markovian control problem as the intensity of the driving Poisson process tends to infinity. We show that the convergence speed is provided by the H\"older constant of the Hessian of…

Optimization and Control · Mathematics 2022-08-19 Marc Abeille , Bruno Bouchard , Lorenzo Croissant

In this paper, we extend the jump-diffusion model proposed by Davis and Lleo to include jumps in asset prices as well as valuation factors. The criterion, following earlier work by Bielecki, Pliska, Nagai and others, is risk-sensitive…

Portfolio Management · Quantitative Finance 2010-03-15 Mark Davis , Sebastien Lleo

This paper studies an optimal stochastic impulse control problem in a finite horizon with a decision lag, by which we mean that after an impulse is made, a fixed number units of time has to be elapsed before the next impulse is allowed to…

Optimization and Control · Mathematics 2021-02-09 Chang Li , Jiongmin Yong

We consider fully nonlinear Hamilton-Jacobi-Bellman equations associated to diffusion control problems involving a finite set-valued (or switching) control and possibly a continuum-valued control. We construct a lower complexity…

Optimization and Control · Mathematics 2016-05-11 Marianne Akian , Eric Fodjo

This paper considers a portfolio optimization problem in which asset prices are represented by SDEs driven by Brownian motion and a Poisson random measure, with drifts that are functions of an auxiliary diffusion factor process. The…

Portfolio Management · Quantitative Finance 2010-11-16 Mark Davis , Sebastien Lleo

We consider stochastic control with discretionary stopping for the drift of a diffusion process over an infinite time horizon. The objective is to choose a control process and a stopping time to minimize the expectation of a convex terminal…

Optimization and Control · Mathematics 2025-06-24 Václav E. Beneš , Georgy Gaitsgori , Ioannis Karatzas

We adopt an optimal-control framework for addressing the undiscounted infinite-horizon discrete-time restless $N$-armed bandit problem. Unlike most studies that rely on constructing policies based on the relaxed single-armed Markov Decision…

Optimization and Control · Mathematics 2024-03-19 Chen YAN

We study non-convex Hamilton-Jacobi equations in the presence of gradient constraints and produce new, optimal, regularity results for the solutions. A distinctive feature of those equations regards the existence of a lower bound to the…

Analysis of PDEs · Mathematics 2020-10-27 Héctor A. Chang-Lara , Edgard A. Pimentel

In this paper we establish periodic homogenization for Hamilton-Jacobi-Bellman (HJB) equations, associated to nonlocal operators of integro-differential type. We consider the case when the fractional diffusion has the same order as the…

Analysis of PDEs · Mathematics 2020-02-24 Adina Ciomaga , Daria Ghilli , Erwin Topp

The focus of this article is studying an optimal control problem for branching diffusion processes. Initially, we introduce the problem in its strong formulation and expand it to include linearly growing drifts. Then, we present a relaxed…

Probability · Mathematics 2026-01-21 Antonio Ocello

This paper studies an optimal dividend problem with a drawdown constraint in a Brownian motion model, requiring the dividend payout rate to remain above a fixed proportion of its historical maximum. This leads to a path-dependent stochastic…

Mathematical Finance · Quantitative Finance 2026-01-08 Chonghu Guan , Jiacheng Fan , Zuo Quan Xu

We consider the problem of finite-horizon optimal control of a discrete linear time-varying system subject to a stochastic disturbance and fully observable state. The initial state of the system is drawn from a known Gaussian distribution,…

Optimization and Control · Mathematics 2017-11-08 Maxim Goldshtein , Panagiotis Tsiotras

In this paper, we investigate infinite horizon jump-diffusion forward-backward stochastic differential equations under some monotonicity conditions. We establish an existence and uniqueness theorem, two stability results and a comparison…

Probability · Mathematics 2016-08-22 Zhiyong Yu

In this paper, we investigate a fully nonlinear evolutionary Hamilton-Jacobi-Bellman (HJB) parabolic equation utilizing the monotone operator technique. We consider the HJB equation arising from portfolio optimization selection, where the…

Mathematical Finance · Quantitative Finance 2021-04-14 Daniel Sevcovic , Cyril Izuchukwu Udeani

We present a theory of optimal control for McKean-Vlasov stochastic differential equations with infinite time horizon and discounted gain functional. We first establish the well-posedness of the state equation and of the associated control…

Optimization and Control · Mathematics 2025-03-27 Silvia Rudà

We consider the optimal dividend problem in the so-called degenerate bivariate risk model under the assumption that the surplus of one branch may become negative. More specific, we solve the stochastic control problem of maximizing…

Probability · Mathematics 2022-08-02 Philipp Lukas Strietzel , Henriette Elisabeth Heinrich

In this paper, we study ergodic backward stochastic differential equations (EBSDEs for short), for which the underlying diffusion is assumed to be multiplicative and of at most linear growth. The fact that the forward process has an…

Probability · Mathematics 2018-01-08 Ying Hu , Florian Lemonnier

We propose a new probabilistic numerical scheme for fully nonlinear equation of Hamilton-Jacobi-Bellman (HJB) type associated to stochastic control problem, which is based on the Feynman-Kac representation in [12] by means of control…

Probability · Mathematics 2019-06-28 Idris Kharroubi , Nicolas Langrené , Huyên Pham

A solution to the optimal problem for determining vector fields which maximize (resp. minimize) the transition probabilities from one location to another for a class of reflecting diffusion processes is obtained in the present paper. The…

Probability · Mathematics 2023-04-27 Zhongmin Qian , Xingcheng Xu