TITLE:
Optimal Portfolios of an Insurer and a Reinsurer under Proportional Reinsurance and Power Utility Preference
AUTHORS:
Silas A. Ihedioha, Bright O. Osu
KEYWORDS:
Proportional Reinsurance, Optimal Investment, Insurer, Reinsurer, Hamilton-Jacobi-Bellman (HJB) Equation, Power Utility Function
JOURNAL NAME:
Open Access Library Journal,
Vol.2 No.12,
December
29,
2015
ABSTRACT:
This study tackled portfolio selection problem for an insurer as well as a
reinsurer aiming at maximizing the probability of survival of the Insurer and
the Reinsurer, to assess the impact of proportional reinsurance on the survival
of insurance companies as well as to determine the condition that would warrant
reinsurance according to the optimal reinsurance proportion chosen by the
insurer. It was assumed the insurer’s and the reinsurer’s surplus processes
were approximated by Brownian motion with drift and the insurer could purchase
proportional reinsurance from the reinsurer and their risk reserves followed
Brownian motion with drift. Obtained were Hamilton-Jacobi-Bellman (HJB)
equations which solutions gave the optimized values of the insurer’s and the
reinsurer’s optimal investments in the risky asset and the value of the
discount rate that would warrant reinsurance as a ratio of their portfolio weights
in the risky asset.