Application of Backward Stochastic Differential Equation in Insurance Mathematics

Abstract

On the condition that an insurance .company is risk neutral, the paper researchs two problems as follows: one is how to arrange reinsurances in order to red uce risk and increase income; the other is how to calculate annual total reserve in order to keep a balance of termin a l financial rev enue and ex penditure. For first problem, proportional reinsurance and excess of loss reinsurance strategies are researched by using the theory of backward stochastic differential equation. According to investment theory, a retained proportion and a retention are obtained on the basis of the explicit solution class of the linear backward stochastic differential equations established for the reinsurances. The res ults have a directly helpful role for insuers to design reinsurances. As for second problem, the paper integrates the ca lcul a ti on of annua l total reserve with return on investment and establishs the linear backward stochastic differential equations of reserve.