Optimal consumption and investment strategies with liquidity risk and lifetime uncertainty for Markov regime-switching jump diffusion models

• Published in: European journal of operational research Vol. 280; no. 3; pp. 1130 - 1143
• Main Authors: Jin, Zhuo, Liu, Guo, Yang, Hailiang
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.02.2020
• Subjects: Lifetime uncertainty; Liquidity risk; Markov chain approximation method; Regime-switching; Stochastic control; Stochastic control; Liquidity risk; Markov chain approximation method; Lifetime uncertainty; Regime-switching
• DOI: 10.1016/j.ejor.2019.07.066
• ISSN: 0377-2217

•An optimal investment and consumption problem for investors of uncertain lifetime is formulated.•Investors’ Investment portfolio are subject to longevity risk, liquid risk and financial risk.•Liquidity risks include random arriving trading opportunities and market liquid state switches.•Liquidity events are triggered by jumps of asset prices and are modeled by Poisson jump processes.•Explicit forms of the optimal consumption and investment strategies are developed. In this paper, we consider the optimal consumption and investment strategies for households throughout their lifetime. Risks such as the illiquidity of assets, abrupt changes of market states, and lifetime uncertainty are considered. Taking the effects of heritage into account, investors are willing to limit their current consumption in exchange for greater wealth at their death, because they can take advantage of the higher expected returns of illiquid assets. Further, we model the liquidity risks in an illiquid market state by introducing frozen periods with uncertain lengths, during which investors cannot continuously rebalance their portfolios between different types of assets. In liquid market, investors can continuously remix their investment portfolios. In addition, a Markov regime-switching process is introduced to describe the changes in the market’s states. Jumps, classified as either moderate or severe, are jointly investigated with liquidity risks. Explicit forms of the optimal consumption and investment strategies are developed using the dynamic programming principle. Markov chain approximation methods are adopted to obtain the value function. Numerical examples demonstrate that the liquidity of assets and market states have significant effects on optimal consumption and investment strategies in various scenarios.