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Survival Probabilities in Compound Poisson Model with Negative Claims and Investments as Viscosity Solutions of Integro-Differential Equationsстатья
Информация о цитировании статьи получена из
Scopus
Дата последнего поиска статьи во внешних источниках: 20 апреля 2022 г.
- Автор: Belkina Tatiana
- Сборник: Springer Proceedings in Mathematics & Statistics
- Серия: Shiryaev A.N., Samouylov K.E., Kozyrev D.V. (eds) Recent Developments in Stochastic Methods and Applications. ICSM-5 2020
- Том: 371
- Год издания: 2021
- Издательство: Springer International Publishing AG
- Местоположение издательства: Cham, Switzerland
- Первая страница: 43
- Последняя страница: 56
- DOI: 10.1007/978-3-030-83266-7_4
- Аннотация: This work relates to the problem of the identifying of some solutions to linear integro-differential equations as the probability of survival (non-ruin) in the corresponding collective risk models involving investments. The equations for the probability of non-ruin as a function of the initial reserve are generated by the infinitesimal operators of corresponding dynamic reserve processes. The direct derivation of such equations is usually accompanied by some significant difficulties, such as the need to prove a sufficient smoothness of the survival probability. We propose an approach that does not require a priori proof of the smoothness. It is based on previously proven facts for a certain class of insurance models with investments: firstly, under certain assumptions, the survival probability is at least a viscosity solution to the corresponding integro-differential equation, and secondly, any two viscosity solutions with coinciding boundary conditions are equivalent. We apply this approach, allowing us to justify rigorously the form of the survival probability, to the collective life insurance model with investments.
- Добавил в систему: Белкина Татьяна Андреевна