Optimal investment and consumption strategies with state-dependent utility functions and uncertain time-horizon

This paper considers the multi-period optimal strategies for an investment-only problem and an investment–consumption problem. The financial market is regime-switching and consists of one risk-free asset and multiple risky assets. The state process of the financial market is modeled by a finite-state Markov chain. Asset returns and utility functions are affected by the states of the financial market. The investment time-horizon is uncertain and exogenous. By adopting the dynamic programming approach, explicit expressions for optimal value functions and optimal investment and consumption strategies are derived. Moreover, some discussions and numerical examples are provided to illustrate our results, which extend some results in the existing literature to more general situations and show some interesting phenomena.

[1]  Multi‐period mean‐variance portfolio selection in a regime‐switching market with a bankruptcy state , 2013 .

[2]  Hailiang Yang,et al.  Optimal investment-consumption strategy in a discrete-time model with regime switching , 2007 .

[3]  R. C. Merton,et al.  Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case , 1969 .

[4]  Süleyman Özekici,et al.  HARA frontiers of optimal portfolios in stochastic markets , 2012, Eur. J. Oper. Res..

[5]  Yan Zeng,et al.  Multi-period mean–variance asset–liability management with uncontrolled cash flow and uncertain time-horizon , 2013 .

[6]  Alex Weissensteiner,et al.  Life-Cycle Asset Allocation and Consumption Using Stochastic Linear Programming , 2007 .

[7]  Wendell H. Fleming,et al.  An Optimal Investment/Consumption Model with Borrowing , 1991, Math. Oper. Res..

[8]  Asset Allocation with Regime-Switching: Discrete-Time Case , 2004, ASTIN Bulletin.

[9]  E. Fama.  Multiperiod Consumption-Investment Decisions , 1970 .

[10]  Suresh P. Sethi,et al.  Explicit Solution of a General Consumption/Investment Problem , 1986, Math. Oper. Res..

[11]  Süleyman Özekici,et al.  Portfolio selection in stochastic markets with HARA utility functions , 2010, Eur. J. Oper. Res..

[12]  R. C. Merton,et al.  Optimum consumption and portfolio rules in a continuous - time model Journal of Economic Theory 3 , 1971 .

[13]  Süleyman Özekici,et al.  Portfolio selection in stochastic markets with exponential utility functions , 2009, Ann. Oper. Res..

[14]  Süleyman Özekici,et al.  Portfolio optimization in stochastic markets , 2006, Math. Methods Oper. Res..

[15]  Zhongfei Li,et al.  Multi-period mean-variance portfolio selection with Markov regime switching and uncertain time-horizon , 2011, J. Syst. Sci. Complex..

[16]  Gang George Yin,et al.  Markowitz's Mean-Variance Portfolio Selection with Regime Switching: A Continuous-Time Model , 2003, SIAM J. Control. Optim..

[17]  T. Zariphopoulou.  Consumption-Investment Models with Constraints , 1994 .

[18]  Abel Cadenillas,et al.  EXPLICIT SOLUTIONS OF CONSUMPTION‐INVESTMENT PROBLEMS IN FINANCIAL MARKETS WITH REGIME SWITCHING , 2009 .

[19]  K. S. Tan,et al.  Multiperiod Optimal Investment-Consumption Strategies with Mortality Risk and Environment Uncertainty , 2008 .

[20]  Claus Munk,et al.  Portfolio and Consumption Choice with Stochastic Investment Opportunities and Habit Formation in Preferences , 2002 .

[21]  Holger Kraft,et al.  Optimal Housing, Consumption, and Investment Decisions over the Life Cycle , 2011, Manag. Sci..

[22]  P. Samuelson.  Lifetime Portfolio Selection by Dynamic Stochastic Programming , 1969 .

[23]  Jinchun Ye,et al.  Optimal life insurance purchase and consumption/investment under uncertain lifetime , 2007 .

[24]  W. Fei.  Optimal consumption and portfolio under inflation and Markovian switching , 2013 .

[25]  Zhongfei Li,et al.  Multi-period portfolio selection for asset-liability management with uncertain investment horizon , 2008 .

[26]  Alex W. H. Chan.  Merton, Robert C. , 2010 .

[27]  Claus Munk.  Optimal consumption/investment policies with undiversifiable income risk and liquidity constraints , 2000 .

[28]  Lionel Martellini,et al.  Static Mean-Variance Analysis with Uncertain Time Horizon , 2006, Manag. Sci..