Optimal consumption-portfolio choices and retirement planning

We examine consumption and investment decisions in a life-cycle model with habit formation, stochastic opportunity set, stochastic wages and labor supply flexibility. We explicitly take account of retirement by specifying an age at which labor earnings stop, but consumption spending continues. Explicit solutions are obtained for optimal consumption, labor supply and the financing portfolio. During the accumulation period the optimal portfolio decomposes into two distinct parts corresponding to the present value of consumption post-retirement and the present value of consumption net of earnings pre-retirement. Surprisingly, the portfolio designed for the exclusive purpose of financing retirement consumption includes hedging components motivated by fluctuations in wages; the part financing pre-retirement consumption is affected by the presence of a retirement period. The effects of a retirement date and of habits on optimal decisions are assessed. We find, in particular, that a public policy decision to postpone the mandatory retirement date could induce an individual to work less and to consume more through most of her life. We also identify conditions under which habit formation reduces consumption and increases labor supply, relative to a model without habits. Finally, we look at the agent's retirement decision. Here the individual derives her utility from consumption/leisure during her working life and wealth at the day of retirement. We allow the agent freely to stop before or at a prespecified final time, in order to maximize the expected utility which we assume to be time separable. A characterization of the agent's optimal retirement region concludes our study.