CAJ | 학술논문

本文考虑了一类相邻两次索赔的时间间隔服从Erlang(n)和Erlang(m)的混合分布的Sparre Andersen风险模型.主要目的是研究Gerber-Shiu函数φ_δ(u),首先证明了φδ(u)满足一个高阶的积分微分方程,然后讨论了广义Lundberg方程根的性质,在此基础上导出了φδ(u)的拉普拉斯变换并且证明了φδ(u)满足一个更新方程,最后给出了一个例子.
본문고필료일류상린량차색배적시간간격복종Erlang(n)화Erlang(m)적혼합분포적Sparre Andersen풍험모형.주요목적시연구Gerber-Shiu함수φ_δ(u),수선증명료φδ(u)만족일개고계적적분미분방정,연후토론료엄의Lundberg방정근적성질,재차기출상도출료φδ(u)적랍보랍사변환병차증명료φδ(u)만족일개경신방정,최후급출료일개례자.
In this paper, we consider a Sparre Andersen risk model in which the claim inter-arrival distribution is a mixture of an Erlang(n) distribution and an Erlang(m) distribution. Our purpose is to study the Gerber-Shiu function φδ(u). First, we show that φδ(u) satisfies a higher-order integro-differential equation, and then we discuss the roots of the generalized Lundberg's equation. On this basis, we drive the Laplace transform of φδ(u) and prove that φδ(u) satisfies a renewal equation. Finally, we consider an example.