Optimal proportional reinsurance and pairs trading under exponential utility criterion for the insurer

Pengxu Xie; Lihua Bai; Huayue Zhang

doi:10.3934/jimo.2022020

Article Contents

2023, Volume 19, Issue 3: 1827-1845. Doi: 10.3934/jimo.2022020

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Optimal proportional reinsurance and pairs trading under exponential utility criterion for the insurer

1.
School of Mathematical Sciences, Nankai University, Tianjin 300071, China
2.
School of Finance, Nankai University, Tianjin 300071, China

^*Corresponding author: Huayue Zhang
^*Corresponding author: Huayue Zhang

Received: September 2021

Revised: December 2021

Early access: February 2022

Published: March 2023

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Abstract

This paper studies the optimal proportional reinsurance and investment strategy for an insurer who invests one paired assets, where their price spread is described by Ornstein-Uhlenbeck (O-U) processes. The insurer's objective is to maximize the expected exponential utility of the terminal wealth in a finite time horizon under two risk models: a classical risk model and a diffusion model. Using the classical stochastic control approach based on the Hamilton-Jacobi-Bellman equation, we characterize the optimal strategies and provide a verification result for the value function via the exponential integrability of the square of an O-U process. Finally, numerical examples are performed to obtain sensitivity analysis.

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Mathematics Subject Classification: Primary: 91G10; Secondary: 93E20.

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Figure 1. The sample path of $ u^* $

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Figure 2. The influence of $ a $ on $ u^* $

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Figure 3. The influence of $ z $ on $ u^* $

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