Optimal consumption and portfolio selection with lower and upper bounds on consumption

Kum-Hwan Roh,Yong Hyun Shin

doi:10.1186/s13662-020-02809-4

Kum-Hwan Roh, Yong Hyun Shin

Open Access

https://doi.org/10.1186/s13662-020-02809-4

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Abstract

We investigate the optimal consumption and investment problem with lower and upper bounds on consumption constraints. We derive closed-form solutions by means of the dynamic programming approach. We also evaluate the effects of the optimal consumption and portfolio on consumption constraints and present some numerical/economic implications. In particular, we see that the upper bound on consumption acts as a bliss level in a quadratic utility model.

Highlights

After Merton’s pioneer research [9, 10] on continuous-time portfolio selection, there have been many studies conducted on the optimal consumption and portfolio selection problem with realistic economic constraints such as borrowing constraints, subsistence consumption constraints, portfolio constraints, etc
Since we have already considered the agent who has a constraint which is acting like a bliss level in quadratic utility [12], we investigate the aspects of the optimal consumption and investment policy of agent when considering an upper bound on consumption
We take the portfolio selection problem into account with the constant upper bound on consumption

Summary

Introduction

After Merton’s pioneer research [9, 10] on continuous-time portfolio selection, there have been many studies conducted on the optimal consumption and portfolio selection problem with realistic economic constraints such as borrowing constraints, subsistence consumption constraints, portfolio constraints, etc. When the optimal consumption and investment problem with quadratic utility is considered, a constant bliss level of consumption depending upon the coefficient of the quadratic utility function can be presented. Since we have already considered the agent who has a constraint which is acting like a bliss level in quadratic utility [12], we investigate the aspects of the optimal consumption and investment policy of agent when considering an upper bound on consumption.

Results

Conclusion