Optimal investment problem for an insurer and a re

Authors: Danping Li Ximin Rong Hui Zhao

Publish Date: 2015/05/27

Volume: 28, Issue: 6, Pages: 1326-1343

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Abstract

This paper studies the optimal investment problem for an insurer and a reinsurer The basic claim process is assumed to follow a Brownian motion with drift and the insurer can purchase proportional reinsurance from the reinsurer The insurer and the reinsurer are allowed to invest in a riskfree asset and a risky asset Moreover the authors consider the correlation between the claim process and the price process of the risky asset The authors first study the optimization problem of maximizing the expected exponential utility of terminal wealth for the insurer Then with the optimal reinsurance strategy chosen by the insurer the authors consider two optimization problems for the reinsurer The problem of maximizing the expected exponential utility of terminal wealth and the problem of minimizing the ruin probability By solving the corresponding HamiltonJacobiBellman equations the authors derive the optimal reinsurance and investment strategies explicitly Finally the authors illustrate the equality of the reinsurer’s optimal investment strategies under the two cases

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