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On Optimal Strategies to Deal with Extreme Regimes in Insurance

Abstract We study a risk model where the insurer’s profit at a finite time horizon τ1 can be controlled by making a change of premium at an optimally chosen time τ < τ1. In the fluid approximation limit, this probabilistic control problem converges in probability to a deterministic problem, which we solve for specific claim size distributions and a unimodal demand function.