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本文研究了一类具有相依结构的风险模型.利用无穷小方法,得到了Gerber-Shiu罚金折现期望函数所满足的积分-微分方程,给出了破产时刻,破产赤字及破产前瞬时盈余的拉普拉斯变换的积分-微分方程的应用.最后,在具有常数红利边界下的同一风险模型中,分析了红利支付的期望现值.
In this paper, a class of risk models with dependent structures is studied. By using the infinitesimal method, the integral-differential equation satisfied by the Gerber-Shiu penalty discounted expectation function is obtained, and the rupture time, the bankruptcy deficit and the pre-bankruptcy surplus are given Laspeyres transform integral-differential equation.Finally, in the same risk model with constant dividend boundary, the expected present value of dividend payment is analyzed.