Disutility, Optimal Retirement, and Portfolio Selection

Abstract

We study the optimal retirement and consumption/investment choice of an infinitelylived economic agent with a time-separable von Neumann-Morgenstern utility. A particular aspect of our problem is that the agent has a retirement option. Before retirement the agent receives labor income but suffers a utility loss from labor. By retiring, he avoids the utility loss but gives up labor income. We show that the agent retires optimally if his wealth exceeds a certain critical level. We also show that the agent consumes less and invests more in risky assets when he has an option to retire than he would in the absence of such an option.An explicit solution can be provided by solving a free boundary value problem. In particular, the critical wealth level and the optimal consumption and portfolio policy are provided in explicit forms.We thank Hyeng Keun Koo, Jaeyoung Sung, and an anonymous refree for helpful comments. Manuscript

Continuous-Time Portfolio Selection: A Cursory Survey

“…Karatzas and Wang [26] make a contribution in this regard by characterizing a condition for the existence of a solution to the mixture problem of optimal stopping and optimal choice of consumption. Choi and Shim [27] study the open problem proposed by Karatzas and Wang [26] in which the agent continues to consume and invest after the retirement. An infinitely-lived live agent chooses optimal retirement time as well as consumption and portfolio.…”

“…Yang and Koo [31] investigate the model of Choi and Shim [27] in a finite horizon with a general period utility function and provide conditions for the existence of a solution and establish properties of optimal policies. Their analysis depends on the theory of partial differential equations (PDEs).…”

“…To understand the portfolio selection problem with retirement option in detail, we explain the problem studied by Choi and Shim [27]. They use dynamic programming.…”

Optimal Stopping and Utility in a Simple Modelof Unemployment Insurance

“…This was complemented by a more general research exploring ways to optimize and improve the efficacy of the UI systems (also in terms of reducing government expenditure), using incentives such as a decreasing benefit throughout the unemployment spell, in conjunction with sanctions and workfare (see [13,17,20,26,27], to cite but a few). A related strand of research is the study of optimal retirement strategies in the presence of involuntary unemployment risks and borrowing constraints [6,7,14,21,40].…”

“…In particular, examples of use of utility in the UI analysis are ubiquitous (see, e.g., [1,2,13,17,19,20,26,27,28]). There have also been efforts to combine optimal stopping and utility [5,6,18,24,32,43]. However, all such examples were limited to using utility functions to re-calculate wealth, while other important objectives and preferences such as the desire to buy the policy or to reduce the waiting times have not been considered as yet, as far as we can tell.…”