Three Essays on Consumption, Retirement, and Asset Allocation

Abstract

I present an optimal life-cycle model with idiosyncratic income risks in which optimal consumption and asset allocation, and optimal retirement strategies are jointly determined. The model sheds new lights on the dynamics of consumption, portfolio, and retirement choice with income risks over the life cycle in an incomplete market and a continuous time setting. This kind of model is new in life-cycle literature, and I develop a new method for solving the life-cycle problem with income risks by using the dynamic programming approach. The integrated theoretical framework suggested by this study can be an economic justification for various empirical observations under reasonably calibrated parameters. Firstly, I develop a new approach for solving the optimal retirement problem for an individual with an unhedgeable income risk. The income risk stems from a forced unemployment event. I introduce a new convex-duality approach for reformulating the original retirement problem and provide an iterative numerical method to solve it. Reasonably calibrated parameters say that this paper can give an explanation for lower consumption and risky investment behaviors of individuals and a relatively higher stock holdings for the poor. I also analyze the sensitivity of an individual's optimal behaviors in changing her wealth level, investment opportunity, and the magnitude of preference for post-retirement leisure. Finally, I find this study explains a procyclical pattern of the number of unemployed job leavers. For the next, I consider an optimal consumption and portfolio choice problem for a retiree who partially annuitized her wealth in the presence of default risk of annuity providers. I develop a new method for solving the optimal consumption and portfolio choice problem in an incomplete financial market. I show that higher default risk may lead retired people to reduce their consumption and increase their stock holdings. I also find that they have a strong demand for selling their life annuities when facing default events of annuity providers. This may provide an alternative explanation for the annuity puzzle. Finally, I study optimal consumption, investment, and retirement strategies of an individual subject to a nonnegative wealth constraint and exposed to unhedgeable forced unemployment risks. I find strong evidence that a small chance of forced unemployment can have a significant effect on the individual's optimal consumption, investment, and retirement behaviors. Comparing a complete market with a private unemployment insurance I show that the market innovation by introduction of private unemployment insurance might increase individuals' welfare, especially welfare of poor people and people with a low post-retirement leisure preference or who are placed in bad economic conditions