Pricing Dynamics and Solvency in Insurance: Capital Allocation, Surplus and Insurance Cycle

Abstract

Abstract This paper proposes a stochastic multi-period pricing model based on the default option value with insurance cycle to examine the interactions among pricing, surplus allocation and solvency for a multiline insurer. The proposed innovative model captures the dynamic aspects of capitalization and the impact of dynamic premium setting on the insurer’s solvency and risk management. We derived the equilibrium premium for different insurance contract designs. Our results show that the allocation of surplus per line affects the default of the other lines and depends on the correlation between the solvency ratio and the loss ratio of the line. The presence of the insurance cycle can boost solvency provided that the insurer adopts the right underwriting strategy. Based on the correlation between the solvency ratio and the loss ratio of the line, the insurer can make strategic decision about fair pricing. This makes it possible to reconcile the objectives of pricing with the insurer’s solvency and its strategic decision-making in a long-term perspective.