A Stochastic Portfolio Optimization Model with Bounded Memory

Mou-Hsiung Chang · Tao Pang · Yipeng Yang

74 citations0/0 files storedMathematics of Operations Research

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Stochastic processes and financial applications Economic theories and models Risk and Portfolio Optimization

Abstract

This paper considers a portfolio management problem of Merton's type in which the risky asset return is related to the return history. The problem is modeled by a stochastic system with delay. The investor's goal is to choose the investment control as well as the consumption control to maximize his total expected, discounted utility. Under certain situations, we derive the explicit solutions in a finite dimensional space.

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References

2000Derivatives in Financial Markets with Stochastic Volatility 2001A solution approach to valuation with unhedgeable risks 1999Risk-Sensitive Dynamic Asset Management 2013Functional Itô calculus and stochastic integral representation of martingales 2010Maximum principle for the stochastic optimal control problem with delay and application 2000Risk‐Sensitive Control and an Optimal Investment Model 2000Some Solvable Stochastic Control Problems With Delay 2003An optimal consumption model with stochastic volatility

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2014Optimal investment–reinsurance with delay for mean–variance insurers: A maximum principle approach 2021A hybrid stochastic differential reinsurance and investment game with bounded memory 2015Optimal investment and excess-of-loss reinsurance problem with delay for an insurer under Heston’s SV model 2020Dynamic asset-liability management problem in a continuous-time model with delay

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