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 a 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.
金卓，博士，澳大利亚墨尔本大学经济系精算中心高级讲师。2005毕业于华中科技大学数学系应用数学专业，获理学学士。2011年毕业于美国韦恩州立大学数学系数学专业，获哲学博士学位。2011年9月至今在澳大利亚墨尔本大学经济系精算中心工作。2014年获得北美精算协会（SOA）准精算师。研究方向为随机最优控制，精算学，数理金融。在国际期刊发表40余篇论文，期刊包括SIAM Journal on Control and Optimization, Automatica, European Journal of Operational Research, Insurance Mathematics and Economics.