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2020, Volume 16, Issue 1: 325-356. Doi: 10.3934/jimo.2018154
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Optimal investment and dividend for an insurer under a Markov regime switching market with high gain tax

  • 1.

    School of Mathematics and Statistics, Anhui Normal University, Wuhu 241002, China

  • 2.

    School of Finance, Nanjing University of Finance and Economics, Nanjing 210023, China

  • 3.

    School of Economics, Nanjing University of Finance and Economics, Nanjing 210023, China

Received:  February 28, 2018
Revised:  April 30, 2018
Early access:  September 2018
Published:  October 2019
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    Abstract

  • This study examines the optimal investment and dividend problem for an insurer with CRRA preference. The insurer's goal is to maximize the expected discounted accumulated utility from dividend before ruin and the insurer subjects to high gain tax payment. Both the surplus process and the financial market are modulated by an external Markov chain. Using the weak dynamic programming principle (WDPP), we prove that the value function of our control problem is the unique viscosity solution to coupled Hamilton-Jacobi-Bellman (HJB) equations with first derivative constraints. Solving an auxiliary problem without regime switching, we prove that, it is optimal for the insurer in a multiple-regime market to adopt the policies in the same way as in a single-regime market. The regularity of the viscosity solution on its domain is proved and thus the HJB equations admits classical solution. A numerical scheme for the value function is provided by the Markov chain approximation method, two numerical examples are given to illustrate the impact of the high gain tax and regime switching on the optimal policies.

    Mathematics Subject Classification: Primary: 93E20; Secondary: 91G80.

    Citation:
    shu

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  • Figure 1.  Comparison of optimal dividend amount

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    Figure 2.  Comparison of optimal investment amount

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    Figure 3.  Optimal dividend amount under bull and bear market

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    Figure 4.  Optimal investment amount under bull and bear marke

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    Table 1.  Parameters setting in Example 1

    (Investor, Parameter)$\mu_1$$\sigma_1$$\mu_2$$\sigma_2$$p$$\beta$$\lambda$$n$
    Merton000.060.30.330.150-
    Financial Agent000.060.30.330.150.210
    Insurer0.40.50.060.30.330.150.210
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    Table 2.  Parameters setting in Example 2

    (State, Parameter)$\mu_1$$\sigma_1$$\mu_2$$\sigma_2$$p$$\beta$$\lambda$$n$
    Bull0.40.50.060.30.30.050.210
    Bear0.30.50.030.30.30.050.210
     | Show Table
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