Optimal investment-reinsurance strategy with derivatives trading under the joint interests of an insurer and a reinsurer

Xia Zhao; Mengjie Li; Qinrui Si; Xia Zhao; Mengjie Li; Qinrui Si

doi:10.3934/era.2022234

Electronic Research Archive

2022, Volume 30, Issue 12: 4619-4634. doi: 10.3934/era.2022234

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Optimal investment-reinsurance strategy with derivatives trading under the joint interests of an insurer and a reinsurer

School of Statistics and Information, Shanghai University of International Business and Economics, Shanghai 201620, China

Received: 28 August 2022 Revised: 05 October 2022 Accepted: 08 October 2022 Published: 31 October 2022

Considering the common interests of an insurer and a reinsurer, the optimal investment-reinsurance problem with derivatives trading is studied. Suppose that both parties would invest a stock and a risk-free asset for capital appreciation, the insurer could purchase reinsurance and trade derivatives, the optimization problem is formulated by maximizing the expected exponential utility of two parties' wealth processes. The corresponding HJB equations are built for optimal strategy through the dynamic programming principle. In addition, derivatives trading is evaluated based on the certainty-equivalence principle. A numerical study directly illustrates how model parameters influence optimal strategies.
- derivatives trading,
- investment-reinsurance,
- HJB equations,
- certainty-equivalence,
- utility function
Citation: Xia Zhao, Mengjie Li, Qinrui Si. Optimal investment-reinsurance strategy with derivatives trading under the joint interests of an insurer and a reinsurer[J]. Electronic Research Archive, 2022, 30(12): 4619-4634. doi: 10.3934/era.2022234

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Abstract

Considering the common interests of an insurer and a reinsurer, the optimal investment-reinsurance problem with derivatives trading is studied. Suppose that both parties would invest a stock and a risk-free asset for capital appreciation, the insurer could purchase reinsurance and trade derivatives, the optimization problem is formulated by maximizing the expected exponential utility of two parties' wealth processes. The corresponding HJB equations are built for optimal strategy through the dynamic programming principle. In addition, derivatives trading is evaluated based on the certainty-equivalence principle. A numerical study directly illustrates how model parameters influence optimal strategies.

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