Optimal Portfolios of an Insurer and a Reinsurer with Proportional Reinsurance through Exponential Utility Maximization under Constant Elasticity of Variance Model

Silas A. Ihedioha^1, , Danat N. Tanko¹ and Dominic P. Shie¹

¹Department of Mathematics, Plateau State University Bokkos, P.M.B 2012 Jos, Plateau state, Nigeria

Cite this paper:
Silas A. Ihedioha, Danat N. Tanko and Dominic P. Shie. Optimal Portfolios of an Insurer and a Reinsurer with Proportional Reinsurance through Exponential Utility Maximization under Constant Elasticity of Variance Model. Journal of Mathematical Sciences and Applications. 2018; 6(1):6-12. doi: 10.12691/jmsa-6-1-2

Abstract

This work studied optimal portfolios of an insurer and a reinsurer under proportional reinsurance and exponential utility preference, aiming at obtaining the optimal strategies for both the insurer and the reinsurer and determined the condition that would warrant reinsurance according to the proportional reinsurance chosen by the insurer and accepted by the reinsurer. The insurer and the reinsurer invested in a market where the price processes of the risky asset adopted constant elasticity of variance (CEV) model and their surplus processes approximated by stochastic differential equations (SDEs). Hamilton-Jacobi-Bellman equations (HJB) were derived and closed form solutions obtained, giving the optimal values of the insurer’s and the reinsurer’s portfolio. Obtained also was the condition for proportional reinsurance.

Keywords:
exponential utility maximization Hamilton-Jacobi-Bellman equations (HJB) insurer and reinsurer optimal strategies stochastic differential equations (SDEs)

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