鞅-等效混合复合泊松过程的表征

IF 1.4 2区数学 Q2 STATISTICS & PROBABILITY

Annals of Applied Probability Pub Date : 2021-04-01 DOI:10.1214/20-AAP1604

D. P. Lyberopoulos, N. D. Macheras

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引用次数: 1

摘要

如果给定的聚合过程S是概率测度P下的混合复合泊松过程，我们给出了P域上所有概率测度Q的刻画，使得P和Q逐渐等价，而S仍然是一个具有改进性质的混合复合泊松过程。这一结果概括了Delbaen & Haezendonck(1989)的早期工作。本文还讨论了在具有风险消失的不存在免费午餐性质的保险市场中与保费计算原则计算有关的含义。

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A characterization of martingale-equivalent mixed compound Poisson processes

If a given aggregate process S is a mixed compound Poisson process under a probability measure P , we provide a characterization of all probability measures Q on the domain of P , such that P and Q are progressively equivalent and S remains a mixed compound Poisson process with improved properties. This result generalizes earlier work of Delbaen & Haezendonck (1989). Implications related to the computation of premium calculation principles in an insurance market possessing the property of no free lunch with vanishing risk are also discussed.

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来源期刊

Annals of Applied Probability 数学-统计学与概率论

CiteScore

2.70

自引率

5.60%

发文量

108

审稿时长

6-12 weeks

期刊介绍： The Annals of Applied Probability aims to publish research of the highest quality reflecting the varied facets of contemporary Applied Probability. Primary emphasis is placed on importance and originality.