This paper presents a new approach for pricing insurance contracts, based both on economic and probabilistic arguments. The novel property of this approach is that it uses the demand for insurance to find the optimal premium an insurer should charge. Our approach stands in contrast to the standard loading factor methods used in actuarial science, where the number of insureds is constant regardless of the charged premium. The insurer maximizes its expected profit, defined as the difference between the expected net revenue from selling insurance contracts and the expected loss due to insolvency. We show how to find the expected-profit maximizing premium, π*, and its corresponding optimal number of insureds, n*. The first proposition presented in our paper identifies the premium (and number of insureds that minimize the expected loss due to insolvency). The second proposition gives, for a broad class of demand curves, sufficient conditions for the existence and uniqueness of an internal optimal solution. The third proposition asserts that, due to the suggested expected loss function, the insurer's objective function demonstrates economies to scale. Lastly, we provide a numerical solution for the case of a linear demand curve, giving the optimal premium and number of insureds.
ASJC Scopus subject areas
- Statistics and Probability
- Economics and Econometrics
- Statistics, Probability and Uncertainty