Optimal investment-reinsurance strategy in the correlated insurance and financial markets

Xiaoyu Xing; Caixia Geng

doi:10.3934/jimo.2021120

Article Contents

2022, Volume 18, Issue 5: 3445-3459. Doi: 10.3934/jimo.2021120

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Optimal investment-reinsurance strategy in the correlated insurance and financial markets

Xiaoyu Xing^, and
Caixia Geng

School of Sciences, Hebei University of Technology, Tianjin 300401, China

^* Corresponding author: Xiaoyu Xing
^* Corresponding author: Xiaoyu Xing

Received: October 2020

Revised: January 2021

Early access: July 2021

Published: September 2022

The first author is supported by NSF grant No.12071107 and State Scholarship Fund 201906705011.

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Abstract

Within the correlated insurance and financial markets, we consider the optimal reinsurance and asset allocation strategies. In this paper, the risk asset is assumed to follow a general continuous diffusion process driven by a Brownian motion, which correlates to the insurer's surplus process. We propose a novel approach to derive the optimal investment-reinsurance strategy and value function for an exponential utility function. To illustrate this, we show how to derive the explicit closed strategies and value functions when the risk asset is the CEV model, 3/2 model and Merton's IR model respectively.

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Mathematics Subject Classification: Primary: 97M30; Secondary: 93E20.

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Figure 1. Effect of $ \beta $ on the optimal strategy $ \pi_s^*(t) $

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Figure 2. Effect of $ \beta_0 $ on the optimal strategy $ \pi_s^*(t) $, when $ \rho=1 $

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Figure 3. Effect of $ \beta_0 $ on the optimal strategy $ \pi_s^*(t) $, when $ \rho=-1 $

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Figure 4. Effect of $ \kappa $ on the optimal strategy $ \pi_s^*(t) $

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Figure 5. Effect of $ \delta $ on the optimal strategy $ \pi_s^*(t) $

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