ABSTRACT

In this paper, we consider a perturbed risk model with stochastic return on investments. After discretizing of the renewal risk process, using the elementary properties of the classical conditional expectation, the Markov property and considerating the ordinary differential equation of a common density function of the inter-arrival times, we introduce a general integro-differential equation for the Laplace transform of the time of ruin with a positive initial surplus. The special cases, for different inter-arrival times distributions, are given in some details in the discrete renewal risk process.

中文翻译：

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具有随机投资回报率的风险模型中的随机演算

摘要

在本文中，我们考虑具有随机投资回报率的扰动风险模型。在将更新风险过程离散化之后，使用经典条件期望的基本性质，马尔可夫性质并考虑到达间隔时间的公共密度函数的常微分方程，我们引入了拉普拉斯的一般积分微分方程初始盈余为正的破产时间的转变。在离散的续签风险过程中，针对到达时间间隔不同的特殊情况进行了详细介绍。