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Analytic-Numerical Investigations of Singular Problems for Survival Probability in the Dual Risk Model with Simple Investment Strategies

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Analytical and Computational Methods in Probability Theory (ACMPT 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10684))

Abstract

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.

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Notes

  1. 1.

    For the SP in the case of risky investments, the formulation of Theorem 2 in [7] contains a mistake: the first condition from (9) is absent therein.

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Author information

Authors and Affiliations

  1. Central Economics and Mathematics Institute of RAS, Moscow, Russia

    T. A. Belkina

  2. Dorodnicyn Computing Center of RAS FRC CSC of RAS, Moscow, Russia

    N. B. Konyukhova

  3. Numerical Technologies Ltd., Kiev, Ukraine

    B. V. Slavko

Authors
  1. T. A. Belkina
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  2. N. B. Konyukhova
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  3. B. V. Slavko
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Corresponding author

Correspondence to T. A. Belkina .

Editor information

Editors and Affiliations

  1. Department of Applied Probability and Informatics, RUDN University, Moscow, Russia

    Vladimir V. Rykov

  2. City University of Hong Kong, Hong Kong, Hong Kong

    Nozer D. Singpurwalla

  3. Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

    Andrey M. Zubkov

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Belkina, T.A., Konyukhova, N.B., Slavko, B.V. (2017). Analytic-Numerical Investigations of Singular Problems for Survival Probability in the Dual Risk Model with Simple Investment Strategies. In: Rykov, V., Singpurwalla, N., Zubkov, A. (eds) Analytical and Computational Methods in Probability Theory. ACMPT 2017. Lecture Notes in Computer Science(), vol 10684. Springer, Cham. https://doi.org/10.1007/978-3-319-71504-9_21

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  • DOI: https://doi.org/10.1007/978-3-319-71504-9_21

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-71503-2

  • Online ISBN: 978-3-319-71504-9

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