Analytic-Numerical Investigations of Singular Problems for Survival Probability in the Dual Risk Model with Simple Investment Strategies
| Autor: | B. V. Slavko, T. A. Belkina, N. B. Konyukhova |
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| Rok vydání: | 2017 |
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| Zdroj: | Analytical and Computational Methods in Probability Theory ISBN: 9783319715032 ACMPT |
| Popis: | We study the life annuity insurance model when simple investment strategies (SISs) of the two types are used: risky investments and risk-free ones. According to a SIS of the first type, the insurance company invests a constant positive part of its surplus into a risky asset while the remaining part is invested in a risk-free asset. A risk-free SIS means that the whole surplus is invested in a risk-free asset. We formulate and study some associated singular problems for linear integro-differential equations (IDEs). For the case of exponential distribution of revenue sizes, we state that survival probabilities as the functions of the initial surplus (IS) are unique solutions of the corresponding problems. Using the results of computational experiments, we conclude that in the region of small sizes of IS the risky SIS may be more effective tool for increasing of the survival probability than risk-free one. |
| Databáze: | OpenAIRE |
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