Mathematical Modelling of an Insurer’s Portfolio and Reinsurance Strategy under the CEV Model and CRRA Utility

One of the major problems encountered by most insurance com panies is portfolio management and payment of claims. Hence the study of optimal portfolio strategy (OPS) and optimal reinsurance strategy (ORS) becomes necessary. In this paper, the insurer is allowed to invest in a risk-free-asset and a risky-asset, where the risky-asset price follows the constant elasticity variance model and can buy proportional reinsurance policy as a backup. By optimal control approach, the Hamilton-Jacobi-Bellman (HJB) equation is obtained. Using Legendre transformation method, the HJB-equation is transformed to a linear partial differential equa tion and solved for OPS and ORS for an insurer with logarithm utility. Finally, numerical and theoretical analyses were presented to study the impact of model parameters on ORS and OPS.