Consumption and Portfolio Selection with Recursive Utility, Stochastic Income, and Liquidity Constraints

40 Pages Posted: 22 Apr 2021 Last revised: 20 Jun 2021

See all articles by Kyoung Jin Choi

Kyoung Jin Choi

University of Calgary - Haskayne School of Business

Minsuk Kwak

Department of Mathematics, Hankuk University of Foreign Studies

Byung Hwa Lim

The University of Suwon - Department of Economics and Finance

Date Written: April 20, 2021

Abstract

This paper studies a continuous-time optimal consumption and portfolio selection problem when an economic agent with recursive utility has stochastic income and liquidity constraints. To tackle this problem, we introduce a transform of the Hamilton-Jacobi-Bellman equation into a free boundary value ODE (ordinary differential equation). This transform is designed to simplify the procedure required for performing a duality method. Then, we characterize the optimal policies by deriving an integral equation with a fixed interval from the free boundary ODE. The integral equation is used to prove the verification theorem and to generate a stable numerical scheme. It is notable that the optimal portfolio depends on the elasticity of intertemporal substitution (EIS) due to liquidity constraints even if the investment opportunity is constant. Furthermore, we perform various analyses to investigate the impact of the borrowing constraints on the optimal policies and the marginal propensity to consume.

Keywords: Recursive utility, liquidity constraints, stochastic income, portfolio optimization

JEL Classification: G11, D14, D91

Suggested Citation

Choi, Kyoung Jin and Kwak, Minsuk and Lim, Byung Hwa, Consumption and Portfolio Selection with Recursive Utility, Stochastic Income, and Liquidity Constraints (April 20, 2021). Available at SSRN: https://ssrn.com/abstract=3831673 or http://dx.doi.org/10.2139/ssrn.3831673

Kyoung Jin Choi

University of Calgary - Haskayne School of Business ( email )

2500 University Drive, NW
Calgary, Alberta T2N 1N4
Canada

HOME PAGE: http://sites.google.com/site/kyoungjinchoiecon/

Minsuk Kwak

Department of Mathematics, Hankuk University of Foreign Studies ( email )

81 Oedae-ro
Yongin, 449-791
Korea, Republic of (South Korea)

Byung Hwa Lim (Contact Author)

The University of Suwon - Department of Economics and Finance ( email )

17 Wauan-gil
Bongdam-eup
Hwaseong, Gyeonggi-do 445-743
+82-10-5007-4310 (Phone)

HOME PAGE: http://https://sites.google.com/site/byunghwalim/

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