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This paper is concerned with a long standing optimal dividend payout problem subject to the so-called ratcheting constraint, that is, the dividend payout rate shall be non-decreasing over time and is thus self-path-dependent. The surplus…

Mathematical Finance · Quantitative Finance 2024-07-08 Chonghu Guan , Zuo Quan Xu

In this article, the notion of viscosity solution is introduced for the path-dependent Hamilton-Jacobi-Bellman (PHJB) equations associated with the optimal control problems for path-dependent stochastic differential equations. We identify…

Optimization and Control · Mathematics 2020-04-07 Jianjun Zhou

We study the optimal investment-consumption problem for a member of defined contribution plan during the decumulation phase. For a fixed annuitization time, to achieve higher final annuity, we consider a variable consumption rate. Moreover,…

Portfolio Management · Quantitative Finance 2020-08-18 Hassan Dadashi

We study the Hamilton-Jacobi equation for undiscounted exit time control problems with general nonnegative Lagrangians using the dynamic programming approach. We prove theorems characterizing the value function as the unique…

Optimization and Control · Mathematics 2007-05-23 Michael Malisoff

This work proposes a novel numerical scheme for solving the high-dimensional Hamilton-Jacobi-Bellman equation with a functional hierarchical tensor ansatz. We consider the setting of stochastic control, whereby one applies control to a…

Numerical Analysis · Mathematics 2025-07-01 Xun Tang , Nan Sheng , Lexing Ying

This paper investigates the optimal control problems for the finite-horizon continuous-time Markov decision processes with delay-dependent control policies. We develop compactification methods in decision processes, and show that the…

Probability · Mathematics 2023-07-06 Zhong-Wei Liao , Jinghai Shao

The purpose of this work is to introduce a notion of weak solution to the master equation of a potential mean field game and to prove that existence and uniqueness hold under quite general assumptions. Remarkably, this is achieved without…

Optimization and Control · Mathematics 2022-06-30 Alekos Cecchin , François Delarue

This paper examines a continuous time intertemporal consumption and portfolio choice problem with a stochastic differential utility preference of Epstein-Zin type for a robust investor, who worries about model misspecification and seeks…

Optimization and Control · Mathematics 2021-03-09 Jiangyan Pu , Qi Zhang

The paper deals with path-dependent Hamilton-Jacobi equations with a coinvariant derivative which arise in investigations of optimal control problems and differential games for neutral-type systems in Hale's form. A viscosity (generalized)…

Optimization and Control · Mathematics 2022-05-10 Anton Plaksin

This paper concerns continuous dependence estimates for Hamilton-Jacobi-Bellman-Isaacs operators (briefly, HJBI). For the parabolic Cauchy problem, we establish such an estimate in the whole space $[0,+\infty)\times\Rn$. Moreover, under…

Analysis of PDEs · Mathematics 2010-08-02 Claudio Marchi

We consider a time-consistent mean-variance portfolio selection problem of an insurer and allow for the incorporation of basis (mortality) risk. The optimal solution is identified with a Nash subgame perfect equilibrium. We characterize an…

Portfolio Management · Quantitative Finance 2019-08-16 Frank Bosserhoff , Mitja Stadje

This paper considers a robust time-consistent mean-variance-skewness portfolio selection problem for an ambiguity-averse investor by taking into account wealth-dependent risk aversion and wealth-dependent skewness preference as well as…

Optimization and Control · Mathematics 2022-01-19 Jian-hao Kang , Nan-jing Huang , Zhihao Hu , Ben-Zhang Yang

This paper first describes a class of uncertain stochastic control systems with Markovian switching, and derives an It\^o-Liu formula for Markov-modulated processes. And we characterize an optimal control law, which satisfies the…

Optimization and Control · Mathematics 2014-01-14 Weiyin Fei

This study investigates an optimal investment problem for an insurance company operating under the Cramer-Lundberg risk model, where investments are made in both a risky asset and a risk-free asset. In contrast to other literature that…

Mathematical Finance · Quantitative Finance 2024-06-25 J. Cerda-Hernandez , A. Sikov , A. Ramos

We study the structure of a simple dynamic optimization problem consisting of one state and one control variable, from a physicist's point of view. By using an analogy to a physical model, we study this system in the classical and quantum…

Mathematical Finance · Quantitative Finance 2017-04-05 Mauricio Contreras , Rely Pellicer , Marcelo Villena

This paper aims to explore the relationship between maximum principle and dynamic programming principle for stochastic recursive control problem with random coefficients. Under certain regular conditions for the coefficients, the…

Optimization and Control · Mathematics 2020-12-10 Yuchao Dong , Qingxin Meng , Qi Zhang

We study a selection problem for degenerate viscous Hamilton--Jacobi equations with convex Hamiltonians, in which the approximation procedure combines a nonlinear discounted approximation with a small potential perturbation. A key question…

Analysis of PDEs · Mathematics 2026-05-14 Qinbo Chen , Zhi-Xiang Zhu

In this paper, we provide an example of the optimal growth model in which there exist infinitely many solutions to the Hamilton-Jacobi-Bellman equation but the value function does not satisfy this equation. We consider the cause of this…

Theoretical Economics · Economics 2024-01-15 Yuhki Hosoya

We present a kernel-based linear matrix inequality (LMI) approach for the approximate solution of Hamilton--Jacobi--Bellman (HJB) equations arising in nonlinear optimal control. The method represents the gradient of the value function in a…

Dynamical Systems · Mathematics 2026-05-19 Boumediene Hamzi , Umesh Vaidya

This paper considers a utility maximization and optimal asset allocation problem in the presence of a stochastic endowment that cannot be fully hedged through trading in the financial market. After studying continuity properties of the…

Portfolio Management · Quantitative Finance 2022-02-24 Christoph Belak , An Chen , Carla Mereu , Robert Stelzer