随机收益下对偶盈余风险模型的推导

Derivation of the Dual Surplus Risk Model under Random Gains

摘要: 本文构建一类含泊松收益到达过程的对偶盈余模型，假定收益间隔服从指数分布、单次收益为独立同分布的随机变量，给出盈余过程的数学表达。通过变量代换、微分求导等分析手段推导模型满足的积分微分方程，刻画盈余过程的演化规律，为后续破产概率、数值仿真与风险度量分析搭建理论基础。研究结果可为创新企业、资源开采类企业的现金流风险管控提供数理分析工具。

Abstract: This paper constructs a dual surplus model with a Poisson gain arrival process, where the inter-arrival times of gains follow an exponential distribution and individual gains are independent and identically distributed random variables, and provides the mathematical formulation of the surplus process. By means of variable substitution, differential derivation and other analytical methods, the integro-differential equation satisfied by the model is derived to characterize the evolution law of the surplus process, which lays a theoretical foundation for subsequent research on ruin probability, numerical simulation and risk measurement. The research results can provide a mathematical analysis tool for cash flow risk management of innovative enterprises and resource exploitation enterprises.