Ruin Probabilities for a Sparre Andersen Model with Investments

On the ruin time distribution for a Sparre Andersen process with exponential claim sizes

We derive a closed-form (infinite series) representation for the distribution of the ruin time for the Sparre Andersen model with exponentially distributed claims. This extends a recent result of Dickson et al. (2005) for such processes with Erlang inter-claim times. We illustrate our result in the cases of gamma and mixed exponential inter-claim time distributions.

分布方程与带有投资的Sparre Andersen模型的破产问题

Distributional equations and the ruin problem for the Sparre Andersen model with investments

本文基于Sparre Andersen模型的投资问题，利用隐含再生理论方法补充了Eberlein等人关于破产概率渐进行为的研究结果。

Sparre-Andersen identity and the last passage time

It is shown that the celebrated result of Sparre Andersen for random walks and Lévy processes has intriguing consequences when the last time of the process in $(-\infty,0]$, say $σ$, is added to the picture. In the case of no positive jumps this leads to six random times, all of which have the same distribution - the uniform distribution on $[0,σ]$. Surprisingly, this result does not appear in the literature, even though it is based on some classical observations concerning exchangeable increments.

破产概率：带有投资的Sparre Andersen模型：年金支付的情况

Ruin Probabilities for a Sparre Andersen Model with Investments: the Case of Annuity Payments

本文扩展了Eberlein等人关于Sparre Andersen非寿险模型破产概率渐近行为的研究，考虑年金支付和双侧跳跃模型。

Optimal Dividend and Investment Problems under Sparre Andersen Model

In this paper we study a class of optimal dividend and investment problems assuming that the underlying reserve process follows the Sparre Andersen model, that is, the claim frequency is a "renewal" process, rather than a standard compound Poisson process. The main feature of such problems is that the underlying reserve dynamics, even in its simplest form, is no longer Markovian. By using the backward Markovization technique we recast the problem in a Markovian framework with expanded dimension representing the time elapsed after the last claim, with which we investigate the regularity of the …

Sparre Andersen 波动定理在可交换且符号不变随机变量上的一个应用

An application of Sparre Andersen's fluctuation theorem for exchangeable and sign-invariant random variables

本文为 Sparre Andersen 关于对称随机游走持续概率的著名结果提供了一个简短证明，适用于可交换且符号不变的随机变量，并将其应用于马尔可夫链对称加性泛函的持续概率研究。