Portfolio Choice and Mortality-Contingent Claims: The General HARA Case

We solve a portfolio choice problem that includes mortality-contingent claims and labor income under general HARA preferences. Our contribution beyond existing literature is to (i) focus on the covariance between shocks to human capital and financial capital, to (ii) model the utility of a family with basic needs and (iii) include life insurance and pension annuity claims in one unified life-cycle model. Our solution employs a "similarity reduction" mapping which reduces the two-dimensional HJB equation into one dimension. This allows for the implementation of a quick numerical scheme. And, when shocks to human capital and financial capital are perfectly correlated, a closed-form expression is obtained as a special case.

[1]  Kevin X. Zhu,et al.  Human Capital, Asset Allocation, and Life Insurance , 2005 .

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

[3]  S. Davis,et al.  Occupation-Level Income Shocks and Asset Returns: Their Covariance and Implications for Portfolio Choice , 2000 .

[4]  Portfolio Choice and Life Insurance: The CRRA Case , 2005 .

[5]  Scott F. Richard,et al.  Optimal consumption, portfolio and life insurance rules for an uncertain lived individual in a continuous time model , 1975 .

[6]  Christian Schlag.  Strategic Asset Allocation: Portfolio Choice for Long‐Term Investors. , 2003 .

[7]  Jérôme Detemple,et al.  Intertemporal asset allocation: A comparison of methods ☆ , 2005 .

[8]  David F. Babbel and Eisaku Ohtsuka..  Aspects of Optimal Multiperiod Life Insurance , 1989 .

[9]  N. H. Hakansson..  OPTIMAL INVESTMENT AND CONSUMPTION STRATEGIES UNDER RISK, AN UNCERTAIN LIFETIME, AND INSURANCE* , 1969 .

[10]  Luis M. Viceira,et al.  Optimal Portfolio Choice for Long-Horizon Investors with Nontradable Labor Income , 1999 .

[11]  David Perry,et al.  A generalized impulse control model of cash management , 2004 .

[12]  Emily Norman Zietz,et al.  An Examination of the Demand for Life Insurance , 2003 .

[13]  R. Jagannathan,et al.  Why should older people invest less in stock than younger people , 1996 .

[14]  M. Berkowitz,et al.  A further look at household portfolio choice and health status , 2006 .

[15]  S. Fischer.  A Life Cycle Model of Life Insurance Purchases , 1973 .

[16]  J. Detemple,et al.  A Monte Carlo Method for Optimal Portfolios , 2000 .

[17]  Hyeng Keun Koo,et al.  Consumption and Portfolio Selection with Labor Income: A Continuous Time Approach , 1998 .

[18]  Michael D. Hurd,et al.  Mortality Risk and Bequests , 1989 .

[19]  J. Heaton,et al.  Portfolio Choice and Asset Prices: The Importance of Entrepreneurial Risk , 2000 .

[20]  Hong Liu,et al.  Lifetime Consumption and Investment: Retirement and Constrained Borrowing , 2009, J. Econ. Theory.

[21]  R. A. Campbell.  The Demand for Life Insurance: An Application of the Economics of Uncertainty , 1980 .

[22]  Zvi Bodie,et al.  Optimal consumption–portfolio choices and retirement planning , 2004 .

[23]  F. Lewis.  Dependents and the Demand for Life Insurance , 1989 .

[24]  S. Sundaresan,et al.  Valuation, Optimal Asset Allocation and Retirement Incentives of Pension Plans , 1997 .

[25]  R. C. Merton,et al.  Labor Supply Flexibility and Portfolio Choice in a Life-Cycle Model , 1992 .

[26]  Michael L. Smith,et al.  Life insurance in a portfolio context , 1983 .

[27]  M. Yaari,et al.  Uncertain lifetime, life insurance, and the theory of the consumer , 1965 .

[28]  C. Peake.  Why Should Older People Invest Less in Stocks than Younger People , 1997 .

[29]  Huaxiong Huang,et al.  Portfolio Choice and Life Insurance: The CRRA Case , 2005 .

[30]  E. Fama,et al.  Human capital and capital market equilibrium , 1977 .

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

[32]  G. William Schwert,et al.  Asset returns and inflation , 1977 .

[33]  Optimal Life Insurance, Consumption and Portfolio under Uncertainty: Martingale Methods , 2007, 2007 American Control Conference.

[34]  Pascal J. Maenhout,et al.  Consumption and Portfolio Choice over the Life Cycle , 2005 .