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We consider a broad class of dynamic programming (DP) problems that involve a partially linear structure and some positivity properties in their system equation and cost function. We address deterministic and stochastic problems, possibly…

Optimization and Control · Mathematics 2026-04-21 Yuchao Li , Dimitri Bertsekas

This paper is concerned with a kind of risk-sensitive optimal control problem for fully coupled forward-backward stochastic systems. The control variable enters the diffusion term of the state equation and the control domain is not…

Optimization and Control · Mathematics 2023-04-11 Jingtao Lin , Jingtao Shi

We consider the approximation of some optimal control problems for the Navier-Stokes equation via a Dynamic Programming approach. These control problems arise in many industrial applications and are very challenging from the numerical point…

Optimization and Control · Mathematics 2022-07-18 Maurizio Falcone , Gerhard Kirsten , Luca Saluzzi

In this paper, we obtain the maximum principle for optimal controls of stochastic systems with jumps by introducing a new method of variation. The control is allowed to enter both diffusion and jump term and the control domain need not to…

Optimization and Control · Mathematics 2019-10-10 Yuanzhuo Song , Shanjian Tang , Zhen Wu

We consider an investor, whose portfolio consists of a single risky asset and a risk free asset, who wants to maximize his expected utility of the portfolio subject to managing the Value at Risk (VaR) assuming a heavy tailed distribution of…

Portfolio Management · Quantitative Finance 2020-12-02 Subhojit Biswas , Mrinal K. Ghosh , Diganta Mukherjee

In this paper, we investigate a sparse optimal control of continuous-time stochastic systems. We adopt the dynamic programming approach and analyze the optimal control via the value function. Due to the non-smoothness of the $L^0$ cost…

Optimization and Control · Mathematics 2021-09-17 Kaito Ito , Takuya Ikeda , Kenji Kashima

We solve an expected utility-maximization problem with a Value-at-risk constraint on the terminal portfolio value in an incomplete financial market due to stochastic volatility. To derive the optimal investment strategy, we use the dynamic…

Portfolio Management · Quantitative Finance 2025-05-21 Marcos Escobar-Anel , Yevhen Havrylenko , Rudi Zagst

We consider the stochastic optimal control problem for the dynamical system of the stochastic differential equation driven by a local martingale with a spatial parameter. Assuming the convexity of the control domain, we obtain the…

Probability · Mathematics 2021-09-15 Jian Song , Meng Wang

The paper concerns the study of the Pontryagin Maximum Principle for an infinite dimensional and infinite horizon boundary control problem for linear partial differential equations. The optimal control model has already been studied both in…

Optimization and Control · Mathematics 2007-11-26 Silvia Faggian

In this paper we consider the maximum principle of optimal control for a stochastic control problem. This problem is governed by a system of fully coupled multi-dimensional forward-backward doubly stochastic differential equation with…

Optimization and Control · Mathematics 2018-09-07 AbdulRahman Al-Hussein , Boulakhras Gherbal

We consider the problem of optimally controlling stochastic, Markovian systems subject to joint chance constraints over a finite-time horizon. For such problems, standard Dynamic Programming is inapplicable due to the time correlation of…

Optimization and Control · Mathematics 2024-11-22 Niklas Schmid , Marta Fochesato , Sarah H. Q. Li , Tobias Sutter , John Lygeros

In this paper, we study backward doubly stochastic recursive optimal control problem where the cost function is described by the solution of a backward doubly stochastic differential equation. We give the dynamical programming principle for…

Probability · Mathematics 2020-08-13 Yunhong Li , Anis. Matoussi , Lifeng Wei , Zhen Wu

We obtain a maximum principle for stochastic control problem of general controlled stochastic differential systems driven by fractional Brownian motions (of Hurst parameter $H>1/2$). This maximum principle specifies a system of equations…

Optimization and Control · Mathematics 2012-03-15 Yuecai Han , Yaozhong Hu , Jian Song

A general stochastic maximum principle is proved for optimal controls of semilinear stochastic evolution equations. Stochastic evolution operators, and the control with values in a general set enter into both drift and diffusion terms.

Optimization and Control · Mathematics 2012-07-03 Kai Du , Qingxin Meng

We shall consider a stochastic maximum principle of optimal control for a control problem associated with a stochastic partial differential equations of the following type: d x(t) = (A(t) x(t) + a (t, u(t)) x(t) + b(t, u(t)) dt +…

Probability · Mathematics 2012-02-20 AbdulRahman Al-Hussein

In this paper, we aim to develop the theory of optimal stochastic control for branching diffusion processes where both the movement and the reproduction of the particles depend on the control. More precisely, we study the problem of…

Probability · Mathematics 2016-09-19 Julien Claisse

In this paper, we study a stochastic recursive optimal control problem in which the system is governed by a functional forward-backward stochastic differential equation. Under standard assumptions, we establish the dynamic programming…

Probability · Mathematics 2013-01-03 Shaolin Ji , Shuzhen Yang

We consider a Bolza-type optimal control problem for a dynamical system described by a fractional differential equation with the Caputo derivative of an order $\alpha \in (0, 1)$. The value of this problem is introduced as a functional in a…

Optimization and Control · Mathematics 2019-08-06 Mikhail I. Gomoyunov

We consider the problem of stochastic optimal control, where the state-feedback control policies take the form of a probability distribution and where a penalty on the entropy is added. By viewing the cost function as a Kullback- Leibler…

Optimization and Control · Mathematics 2024-12-12 Marc Lambert , Francis Bach , Silvère Bonnabel

We study a stochastic control problem on a bounded domain, which arises from a continuous-time optimal management model. Via the corresponding Hamilton-Jacobi-Bellman equation the value function is shown to be jointly continuous and to…

Probability · Mathematics 2017-10-24 Ruoting Gong , Christian Houdré