The Optimal Deductible and Coverage in Insurance Contracts and Equilibrium Risk Sharing Policies

In this paper, we consider the optimal risk sharing problem between two parties in the insurance business: the insurer and the insured. The risk is allocated between the insurer and the insured by setting a deductible and coverage in the insurance contract. We obtain the optimal deductible and coverage by considering the expected product of the two parties' utilities of terminal wealth according to stochastic optimal control theory. An equilibrium policy is also derived for when there are both a deductible and coverage; this is done by modelling the problem as a stochastic game in a continuous-time framework. A numerical example is provided to illustrate the results of the paper.

Automated summary

This paper investigates the optimal risk sharing problem between the insurer and the insured in the insurance business. The risk is allocated by setting a deductible and coverage in the insurance contract. The optimal deductible and coverage are obtained using stochastic optimal control theory. An equilibrium policy is derived by modeling the problem as a stochastic game in a continuous-time framework. A numerical example is provided to illustrate the findings of the paper.