Consumption-Portfolio Optimization with Regime-Switching-Modulated Habit Formation and Jump Diffusion

• 成果类型: Article; Early Access
• 署名作者: Wang, Yike; Liu, Jingzhen; Yiu, Ka-Fai Cedric; Siu, Tak Kuen
• 署名单位: Chongqing Technology & Business University; Central University of Finance & Economics; Hong Kong Polytechnic University; Macquarie University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X; 1526-5471
• DOI: 10.1287/moor.2024.0771
• 发表日期: 2026-04-22
• 关键词: consumption portfolio; habit formation; regime switching; Jump diffusion; backward stochastic partial differential equation; Utility maximization; INVESTMENT; selection; MARKETS; prices

摘要

This paper studies consumption-portfolio optimization problems with habit formation in a regime-switching market. The habit level, which reflects the endogenous impact of past consumption, also involves regime switching and jump diffusion. Because of the presence of general utility functions and path-dependent random parameters, we use the market completion method and introduce some additional jump assets to address the problems. After reducing the problems to solving a stochastic Hamilton-Jacobi-Bellman equation, we derive the optimal control by a joint adoption of envelope theorem and backward stochastic partial differential equation. In general, the optimal portfolio strategy includes the demand of jump assets for hedging against the regime-switching and jumpdiffusion risk. In particular, for power/logarithmic utility, we obtain a closed-form solution in the enlarged complete market. For comparison, we also study the power/logarithmic utility case with many specific conditions in the primal incomplete market by restricting the positions of the jump assets to zero.