Robust optimal excess-of-loss reinsurance and investment problem with <i>p</i>-thinning dependent risks under CEV model

Lei Mao; Yan Zhang; Lei Mao; Yan Zhang

doi:10.3934/QFE.2021007

Quantitative Finance and Economics

2021, Volume 5, Issue 1: 134-162. doi: 10.3934/QFE.2021007

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Robust optimal excess-of-loss reinsurance and investment problem with p-thinning dependent risks under CEV model

Lei Mao ^{1,2
,
,},
Yan Zhang ²

1.
School of Mathematical Sciences, Institute of Mathematics, Nanjing Normal University, Nanjing 210023, China
2.
Department of General Education, Army Engineering University of PLA, Nanjing 211101, China

Received: 29 November 2020 Accepted: 19 February 2021 Published: 22 February 2021
JEL Codes: G32

This paper is devoted to study a robust optimal excess-of-loss reinsurance and investment problem with p-thinning dependent risks for an ambiguity-averse insurer (AAI). Assume that the AAI's wealth process consists of two p-thinning dependent classes of insurance business. The AAI is allowed to purchase excess-of-loss reinsurance and invest in a financial market consisting of one risk-free asset and one risky asset, where risky asset's price follows CEV model. Under the criterion of maximizing the expected exponential utility of AAI's terminal wealth, the explicit expressions of the optimal excess-of-loss reinsurance and investment strategy are derived by employing techniques of stochastic control theory. Moreover, we provide the verification theorem and present some numerical examples to analyze the impacts of parameters on our optimal control strategies.
- CEV model,
- excess-of-loss reinsurance,
- thinning,
- dependent,
- ambiguity-averse
Citation: Lei Mao, Yan Zhang. Robust optimal excess-of-loss reinsurance and investment problem with p-thinning dependent risks under CEV model[J]. Quantitative Finance and Economics, 2021, 5(1): 134-162. doi: 10.3934/QFE.2021007

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Abstract

This paper is devoted to study a robust optimal excess-of-loss reinsurance and investment problem with p-thinning dependent risks for an ambiguity-averse insurer (AAI). Assume that the AAI's wealth process consists of two p-thinning dependent classes of insurance business. The AAI is allowed to purchase excess-of-loss reinsurance and invest in a financial market consisting of one risk-free asset and one risky asset, where risky asset's price follows CEV model. Under the criterion of maximizing the expected exponential utility of AAI's terminal wealth, the explicit expressions of the optimal excess-of-loss reinsurance and investment strategy are derived by employing techniques of stochastic control theory. Moreover, we provide the verification theorem and present some numerical examples to analyze the impacts of parameters on our optimal control strategies.

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