Optimal Probability of Survival of an Insurer and a Reinsurer under Proportional Reinsurance and Power Utility Preference
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- Hamilton Jacobi Bellman HJB Equation, Insurer, Optimal Investment, Power Utility Function, Probability Of Survival, Proportional Reinsurance, Reinsurer
- Silas A. Ihedioha; Bright O. Osu
- This study assumed the risk reserve of an insurer and a reinsurer to follow Brownian motion with drift and tackled their optimal probability of survival problem under proportional reinsurance and power utility preference. The insurer’s and reinsurer’s surplus processes are approximated by Brownian motion with drift and the insurer can purchase proportional reinsurance from a reinsurer. In addition, the insurer and reinsurer are allowed to invest in one risky and one risk-free, assets. We obtained by solving the corresponding Hamilton-Jacobi-Bellman (HJB) equations, the optimized values of the insurer and the reinsurer, optimal investment in the risky asset by both of them and then solved for the discount value, ϕ, that would warrant reinsurance, according to the optimal reinsurance proportion chosen by the insurer.
Full text: IJISM_479_Final.pdf