A stochastic portfolio optimization model with complete memory. Issue 4 (4th July 2017)

• Record Type: Journal Article
• Authors: Pang, Tao; Hussain, Azmat
• Is Part Of: Stochastic analysis and applications. Volume 35:Issue 4(2017)
• Page Start: 742
• Page End: 766
• Publication Date: 2017-07-04
• Subjects: Portfolio optimization -- Hamilton–Jacobi–Bellman equation -- dynamic programming -- stochastic delay equation; 91G80 -- 93E20 -- 60H30 -- 34K50 -- 49L20; Stochastic analysis -- Periodicals; 519.2205
• DOI: 10.1080/07362994.2017.1299629
• Languages: English
• ISSNs: 0736-2994

Abstract

ABSTRACT: In this article, we consider a portfolio optimization problem of the Merton's type with complete memory over a finite time horizon. The problem is formulated as a stochastic control problem on a finite time horizon and the state evolves according to a process governed by a stochastic process with memory. The goal is to choose investment and consumption controls such that the total expected discounted utility is maximized. Under certain conditions, we derive the explicit solutions for the associated Hamilton–Jacobi–Bellman (HJB) equations in a finite-dimensional space for exponential, logarithmic, and power utility functions. For those utility functions, verification results are established to ensure that the solutions are equal to the value functions, and the optimal controls are also derived.