Optimal investment, consumption and retirement choice problem with disutility and subsistence consumption constraints

Abstract

In this paper we consider a general optimal consumption-portfolio selection problem of an infinitely-lived agent whose consumption rate process is subject to subsistence constraints before retirement. That is, her consumption rate should be greater than or equal to some positive constant before retirement. We integrate three optimal decisions which are the optimal consumption, the optimal investment choice and the optimal stopping problem in which the agent chooses her retirement time in one model. We obtain the explicit forms of optimal policies using a martingale method and a variational inequality arising from the dual function of the optimal stopping problem. We treat the optimal retirement time as the first hitting time when her wealth exceeds a certain wealth level which will be determined by a free boundary value problem and duality approaches. We also derive closed forms of the optimal wealth processes before and after retirement. Some numerical examples are presented for the case of constant relative risk aversion (CRRA) utility class.

Stochastic portfolio optimization with default risk

“…Since then, default-free portfolio optimization models have been extensively investigated in the literature (see, e.g., [4][5][6][7][8][9][10][11] and references therein). In [4], Fleming and Pang discussed a classical Merton portfolio optimization problem, where the interest rate r was assumed to be an ergodic Markov diffusion process.…”

Comparison of optimal portfolios with and without subsistence consumption constraints

“…This constraint is defined as the inequality that an agent's consumption rate should be greater than or equal to a certain positive constant. In [4][5][6][7][8], they solved the portfolio optimization problem with subsistence constraints. There are also many types of portfolio constraints but we do not mention these constraints because we only have our attention on consumption constraints, especially, the subsistence constraints.…”

“…We want to figure out how the subsistence consumption constraints affect the agent's economic behavior concretely. Focusing on the optimal investment, we compare the results of two papers, [14,7]. In [14] (hereafter, CS), they considered a general optimal consumption and investment problem in which a working agent has an option to retire.…”

“…They obtained closed-form solutions and derived numerical results for a constant relative risk aversion (CRRA) utility function. In [7] (hereafter, LSC), the results of CS' model are expanded to the model with subsistence consumption constraints. The closed-form solutions and numerical results were also obtained.…”

Optimal portfolio, consumption and retirement decision under a preference change

“…Especially optimal consumptionportfolio selection problems with option to retire have been also considered under the framework of discretionary stopping time problems suggested by Karatzas and Wang [11]. (See [1][2][3]5] and [12].) On the other hand, under the framework of the Markov decision processes, Filar et al [6] considered the optimal retirement time as a target hitting time.…”