Price vs. Reserve Regulation Conditioned by Solvency Requirements in the Collective Risk Model

The balance of policy prices vs. reserves conditioned by solvency requirements is considered, aiming analysis of an insurer as subject of price competitive insurance market. The intrinsic relationship between the policy prices and the risk reserves, and the influence of this balance on solvency of individual insurance business are formalized in the framework of the collective risk model. Different approaches to tuning prices vs. reserves conditioned by solvency requirements expressed in terms of the probability of ruin within finite time and of the ultimate probability of ruin, based on (a) exact numerical technique, (b) new approximations, and (c) simulation, are discussed.

KEYWORDS: Solvency of insurer, Capital requirements, Price competition, Finite time and ultimate ruin probabilities, Exact numerical technique, Approximations, Simulation.