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In this article we study a finite horizon optimal control problem with monotone controls. We consider the associated Hamilton-Jacobi-Bellman (HJB) equation which characterizes the value function. We consider the totally discretized problem…

Optimization and Control · Mathematics 2014-07-08 Eduardo A. Philipp , Laura S. Aragone , Lisandro A. Parente

We study a consumption-investment problem in a multi-asset market where the returns follow a generic rank-based model. Our main result derives an HJB equation with Neumann boundary conditions for the value function and proves a…

Mathematical Finance · Quantitative Finance 2025-10-24 David Itkin

This paper studies the continuous time utility maximization problem on consumption with addictive habit formation in incomplete semimartingale markets. Introducing the set of auxiliary state processes and the modified dual space, we embed…

Portfolio Management · Quantitative Finance 2015-05-29 Xiang Yu

We determine the optimal robust investment strategy of an individual who targets at a given rate of consumption and seeks to minimize the probability of lifetime ruin when she does not have perfect confidence in the drift of the risky…

Optimization and Control · Mathematics 2014-11-04 Erhan Bayraktar , Yuchong Zhang

We investigate optimal consumption and investment problems for a Black-Scholes market under uniform restrictions on Value-at-Risk and Expected Shortfall. We formulate various utility maximization problems, which can be solved explicitly. We…

Portfolio Management · Quantitative Finance 2010-02-15 Claudia Kluppelberg , Serguei Pergamenchtchikov

A continuous-time consumption-investment model with constraint is considered for a small investor whose decisions are the consumption rate and the allocation of wealth to a risk-free and a risky asset with logarithmic Brownian motion…

Portfolio Management · Quantitative Finance 2022-01-06 Zuo Quan Xu , Fahuai Yi

In this work we study a finite horizon optimal liquidation problem with multiplicative price impact in algorithmic trading, using market orders. We analyze the case when an agent is trading on a market with two financial assets, whose…

Optimization and Control · Mathematics 2020-10-07 Riccardo Cesari , Harry Zheng

We study the well-posedness of Hamilton-Jacobi-Bellman equations on subsets of $\mathbb{R}^d$ in a context without boundary conditions. The Hamiltonian is given as the supremum over two parts: an internal Hamiltonian depending on an…

Analysis of PDEs · Mathematics 2021-04-05 Richard C. Kraaij , Mikola C. Schlottke

In this paper we study the optimization problem of an economic agent who chooses a job and the time of retirement as well as consumption and portfolio of assets. The agent is constrained in the ability to borrow against future income. We…

Optimization and Control · Mathematics 2021-07-28 Junkee Jeon , Hyeng Keun Koo

This study investigates a stochastic production planning problem with a running cost composed of quadratic production costs and inventory-dependent costs. The objective is to minimize the expected cost until production stops when inventory…

Optimization and Control · Mathematics 2025-05-20 Dragos-Patru Covei

An optimal control problem is considered for a stochastic differential equation containing a state-dependent regime switching, with a recursive cost functional. Due to the non-exponential discounting in the cost functional, the problem is…

Optimization and Control · Mathematics 2017-12-29 Hongwei Mei , Jiongmin Yong

We show that necessary and sufficient conditions of optimality in periodic optimization problems can be stated in terms of a solution of the corresponding HJB inequality, the latter being equivalent to a max-min type variational problem…

Optimization and Control · Mathematics 2013-09-10 Vladimir Gaitsgory , Ludmila Manic

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

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

This paper, which is the natural continuation of a previous paper by the same authors, studies a class of optimal control problems with state constraints where the state equation is a differential equation with delays. This class includes…

Optimization and Control · Mathematics 2009-07-10 Salvatore Federico , Ben Goldys , Fausto Gozzi

In this paper, we consider a company can simultaneously reduce its emissions and buy carbon allowances at any time. We establish an optimal control model involving two stochastic processes with two control variables, which is a singular…

Optimization and Control · Mathematics 2024-07-12 Xinfu Chen , Yuchao Dong , Wenlin Huang , Jin Liang

We study a continuous-time portfolio choice problem for an investor whose state-dependent preferences are determined by an exogenous factor that evolves as an It\^o diffusion process. Since risk attitudes at the end of the investment…

Mathematical Finance · Quantitative Finance 2025-12-25 Luca De Gennaro Aquino , Sascha Desmettre , Yevhen Havrylenko , Mogens Steffensen

Many optimal control problems are formulated as two point boundary value problems (TPBVPs) with conditions of optimality derived from the Hamilton-Jacobi-Bellman (HJB) equations. In most cases, it is challenging to solve HJBs due to the…

Optimization and Control · Mathematics 2019-07-25 Sixiong You , Ran Dai , Ping Lu

In this paper we consider a pairs trading financial market with the spread of risky assets defined by the Ornstein-Uhlenbeck (OU) process. We implement an optimal strategy for power utility functions for investment/consumption problem.…

Probability · Mathematics 2018-09-24 Sahar Albosaily , Serge Pergamenshchikov

The paper studies a system of Hamilton-Jacobi equations, arising from a stochastic optimal debt management problem in an infinite time horizon with exponential discount, modeled as a noncooperative interaction between a borrower and a pool…

Optimization and Control · Mathematics 2019-10-29 Rossana Capuani , Steven Gilmore , Khai T. Nguyen