Equilibrium investment and risk control for an insurer with non-Markovian regime-switching and no-shorting constraints

Hui Sun; Zhongyang Sun; Ya Huang; Hui Sun; Zhongyang Sun; Ya Huang

doi:10.3934/math.2020449

AIMS Mathematics

2020, Volume 5, Issue 6: 6996-7013. doi: 10.3934/math.2020449

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Research article

Equilibrium investment and risk control for an insurer with non-Markovian regime-switching and no-shorting constraints

1.
College of Transportation, Shandong University of Science and Technology, Qingdao, Shandong 266590, China
2.
School of Statistics, Qufu Normal University, Qufu, Shandong 273165, China
3.
School of Business, Hunan Normal University, Changsha, Hunan 410081, China

Received: 11 June 2020 Accepted: 03 September 2020 Published: 09 September 2020
MSC : 62P05, 93E20

In this paper, we study the time-consistent equilibrium investment and risk control policies for an insurer under the mean-variance criterion. The dynamics of liability and assets are given by non-Markovian regime-switching models driven by a Brownian motion and a continuous time finite-state Markov chain. It is assumed that the insurer has a time-varying preference of risk depending dynamically on current wealth, and is not allowed to short sell the risky assets. With the aid of backward stochastic differential equations and bounded mean oscillation martingales, we obtain feedback representations of the open-loop equilibrium strategies. Finally, the result is also applied to solve an example of the Markovian regime-switching model.
Citation: Hui Sun, Zhongyang Sun, Ya Huang. Equilibrium investment and risk control for an insurer with non-Markovian regime-switching and no-shorting constraints[J]. AIMS Mathematics, 2020, 5(6): 6996-7013. doi: 10.3934/math.2020449

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Abstract

In this paper, we study the time-consistent equilibrium investment and risk control policies for an insurer under the mean-variance criterion. The dynamics of liability and assets are given by non-Markovian regime-switching models driven by a Brownian motion and a continuous time finite-state Markov chain. It is assumed that the insurer has a time-varying preference of risk depending dynamically on current wealth, and is not allowed to short sell the risky assets. With the aid of backward stochastic differential equations and bounded mean oscillation martingales, we obtain feedback representations of the open-loop equilibrium strategies. Finally, the result is also applied to solve an example of the Markovian regime-switching model.

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