Optimal investment and consumption in the market with jump risk and capital gains tax

Yong Ma; Shiping Shan; Weidong Xu

doi:10.3934/jimo.2018130

Article Contents

2019, Volume 15, Issue 4: 1937-1953. Doi: 10.3934/jimo.2018130

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Optimal investment and consumption in the market with jump risk and capital gains tax

1.
College of Finance and Statistics, Hunan University, Changsha 410079, China
2.
School of Management, Zhejiang University, Hangzhou 310085, China

* Corresponding author: Weidong Xu. Tel.: +86-0571-88206867
* Corresponding author: Weidong Xu. Tel.: +86-0571-88206867

Received: March 2018

Revised: May 2018

Early access: August 2018

Published: July 2019

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Abstract

This paper investigates the problem of dynamic investment and consumption in a market, where a risky asset evolves with jumps and capital gains are taxed. In addition, the investor's behavior of tax evasion is taken into account, and tax evasion is subject to penalty when it is uncovered by audits. Using dynamic programming approach, we derive an analytical solution for an investor with the CRRA utility. We find the following: (1) jumps in the risky asset do not affect the optimal tax evasion strategy; (2) jump risk lessens the optimal fraction of wealth in the risky asset; (3) tax evasion can be reduced by increasing the fine and/or the frequency of tax audits; (4) the effects of the jumps, audits and penalty on the optimal consumption are determined by the degree of risk aversion of the investor.

Keywords:

Mathematics Subject Classification: Primary: 93E20, 93E03; Secondary: 90C39.

Citation:

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Figure 1. Dynamic optimal investment and consumption

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Figure 2. The effect of jump intensity of asset price on optimal investment and consumption

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Figure 3. The effect of jump mean of asset price on optimal investment and consumption

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Figure 4. The effect of tax policy on optimal investment and consumption ($\gamma>1$)

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Table 1. The values of the parameters in the base case

Parameter	Value	Parameter	Value
Current time	$t=0$	Terminal time	$T=20$
Expected return	$\mu=0.08$	Volatility	$\sigma=0.2$
Riskless interest rate	$r=0.04$	Risk aversion coefficient	$\gamma=2.5$
Discount factor	$\rho=0.04$	Relative weight	$\chi=1$
Audit intensity	$\lambda_2=0.1$	Punishment intensity	$\alpha=0.08$
Tax rate on riskless asset	$\tau_G=0.27$	Tax rate on risky asset	$\tau=0.235$
Jump intensity	$\lambda_1=0.15$	Log jump mean	$\mu_J=0$
Jump volatility	$\sigma_J=0.5$

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