An insurance company entering the property and liability insurance market at the high point of the insurance cycle may decide to slash premiums to gain an advantageous market share. Such aggressive intrusion may call forth a concerted industry response, producing a severe decline in the insurance market price. This can ruin some companies, and agrees with the observation that the insurance cycles are correlated with clustered insolvencies. This paper addresses a quantitative analysis of competition-originated cycles; it explores an interplay of rational aggressive and defensive strategies in the multi-period Lundberg-type controlled risk model.
