Optimal Portfolio, Consumption‐leisure and Retirement Choice Problem With Ces Utility

Abstract

We study optimal portfolio, consumption-leisure and retirement choice of an infinitely lived economic agent whose instantaneous preference is characterized by a constant elasticity of substitution (CES) function of consumption and leisure. We integrate in one model the optimal consumption-leisure-work choice, the optimal portfolio selection, and the optimal stopping problem in which the agent chooses her retirement time. The economic agent derives utility from both consumption and leisure, and is able to adjust her supply of labor flexibly above a certain minimum work-hour, and also has a retirement option. We solve the problem analytically by considering a variational inequality arising from the dual functions of the optimal stopping problem. The optimal retirement time is characterized as the first time when her wealth exceeds a certain critical level. We provide the critical wealth level for retirement and characterize the optimal consumption-leisure and portfolio policies before and after retirement in closed forms. We also derive properties of the optimal policies. In particular, we show that consumption in general jumps around retirement.We are grateful to two anonymous referees and an associate editor for helpful comments and advice. We also appreciate Hyeng Keun Koo for helpful comments.Manuscript

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

“…(See Remark 3.1 of Choi and Koo [2], Remark 3.1 of Choi et al [4] and Proposition 2.4 of Jeanblanc et al [9].) That is, for (7) is given by…”

“…We derive the explicit forms of optimal policies using a martingale method and a variational inequality arising from the dual function of the optimal stopping problem under the framework of Karatzas and Wang [13]. The optimal retirement time τ suggested by Choi and Koo [2], Choi and Shim [3], Farhi and Panageas [6] and Choi et al [4] is considered 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 the optimal wealth processes before and after retirement in closed forms.…”

Optimal portfolio, consumption and retirement decision under a preference change

“…(See Proposition 2.4 of Jeanblanc, Lakner, and Kadam [7], Section 3 of Choi and Koo [1] and Remark 3.1 of Choi, Shim, and Shin [3]. )…”

“…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.…”

Social Security Benefit Valuation, Risk, and Optimal Retirement

“…Although we focus on optimizing the present value of future Social Security benefits, we note that circumstances may arise where a beneficiary may have a different financial goal in mind. For example, in (Choi et al 2008), the authors considered optimal portfolio construction, while taking into account the retirement consumption and leisure utility of the beneficiary. In (Huang et al 2012), the interplay between the consumption rate of the retirement savings of a beneficiary and simultaneous health status was modeled as a stochastic process.…”