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Risk-Free Investments and Their Comparison with Simple Risky Strategies in Pension Insurance Models: Solution of Singular Problems for Integro-differential Equations 2020, Vol. 60, No. 10, pp. 1621–1641статья Исследовательская статья
- Авторы: Belkina T.A., Konyukhova N.B., Slavko B.V.
- Журнал: Computational Mathematics and Mathematical Physics
- Том: 60
- Номер: 10
- Год издания: 2020
- Издательство: Pleiades Publishing, Ltd
- Местоположение издательства: Road Town, United Kingdom
- Первая страница: 1621
- Последняя страница: 1641
- DOI: 10.1134/S096554252010005X
- Аннотация: A collective pension insurance (life annuity) model is investigated in the case of risk-freeinvestments, i.e., when the whole surplus of an insurance company at each time is invested in risk-freeasset (bank account). This strategy is compared with previously studied simple risky investment strategies,according to which, irrespective of the surplus of an insurance company, a constant positivefraction of this surplus at each time consists of risky assets (stocks), while the remaining fraction isinvested in a bank account. The strategies are compared in terms of a traditional solvency criterion,namely, the survival probability. The original insurance model is dual to the classical Cramér–Lundbergmodel: the variation in the surplus over the portfolio of same-type contracts is described by thesum of a decreasing deterministic linear function corresponding to total pension payments and a compoundPoisson process with positive jumps corresponding to the income gained by the company at themoments of transferring policyholders' property. In the case of an exponential jump size distributionand risk-free investments, it is shown that the survival probability regarded as a function of the initialsurplus defined on the nonnegative real half-line is a solution of a singular problem for an integro-differentialequation with a non-Volterra integral operator. The solution of the stated problem isobtained, its properties are analytically examined, and numerical examples are given. Examples areused to compare the influence exerted by risky and risk-free investments on the survival probability inthe given model.
- Добавил в систему: Белкина Татьяна Андреевна