保留化合物混合更新过程结构的渐进等效概率测度的表征

IF 0.6 4区数学 Q4 STATISTICS & PROBABILITY

Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2020-07-10 DOI:10.30757/alea.v20-09

Spyridon M. Tzaninis, N. D. Macheras

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引用次数: 2

摘要

对于给定的概率测度P下的复合混合更新过程S，我们推广了Delbaen & Haezendonck[5]以及[18]和[16]的早期工作，在P域上刻画了所有这些概率测度Q，使得Q和P逐渐等价，并且S仍然是Q下具有改进性质的复合混合更新过程。因此，我们证明了任何复合混合更新过程都可以通过改变措施转化为复合混合泊松过程。在[26]和[27]中分别讨论了破产问题和保险市场中没有套利机会的保费计算原则的计算。

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A characterization of progressively equivalent probability measures preserving the structure of a compound mixed renewal process

Generalizing earlier works of Delbaen & Haezendonck [5] as well as of [18] and [16] for given compound mixed renewal process S under a probability measure P, we characterize all those probability measures Q on the domain of P such that Q and P are progressively equivalent and S remains a compound mixed renewal process under Q with improved properties. As a consequence, we prove that any compound mixed renewal process can be converted into a compound mixed Poisson process through a change of measures. Applications related to the ruin problem and to the computation of premium calculation principles in an insurance market without arbitrage opportunities are discussed in [26] and [27], respectively.

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来源期刊

Alea-Latin American Journal of Probability and Mathematical Statistics STATISTICS & PROBABILITY-

CiteScore

1.10

自引率

0.00%

发文量

期刊介绍： ALEA publishes research articles in probability theory, stochastic processes, mathematical statistics, and their applications. It publishes also review articles of subjects which developed considerably in recent years. All articles submitted go through a rigorous refereeing process by peers and are published immediately after accepted. ALEA is an electronic journal of the Latin-american probability and statistical community which provides open access to all of its content and uses only free programs. Authors are allowed to deposit their published article into their institutional repository, freely and with no embargo, as long as they acknowledge the source of the paper. ALEA is affiliated with the Institute of Mathematical Statistics.