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Wealth Investment Strategies for Insurance Companies and the Probability of Ruin

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Abstract

This work is focused on the formulation of the wealth, analysis of the continuous- and discrete-time investment strategies in risky as well as risk-free markets and the probability of ruin for insurance companies. We also discuss solvency condition for each investment strategy and obtain explicit expression for the probability of ruin of a particular investments strategy. Moreover, we identify maximum claim size which would not produce ruin when investments are made.

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References

  • Albrecher H, Constantinescu C, Thomann E (2012) Asymptotic results for renewal risk models with risky investments. Stoch Process Appl 122(11):3767–3789

    Article  MathSciNet  MATH  Google Scholar 

  • Albrecher H, Constantinescu C, Palmowski Z, Regensburger G, Rosenkranz M (2013) Exact and asymptotic results for insurance risk models with surplus-dependent premiums. SIAM J Appl Math 73(1):47–66

    Article  MathSciNet  MATH  Google Scholar 

  • Andersen ES (1957) On the collective theory of risk in case of contagion between claims. Bull Inst Math Appl 12:275–279

    Google Scholar 

  • Asmussen S, Albrecher H (2010) Ruin probabilities (Vol. 14). Singapore, World scientific

    Book  MATH  Google Scholar 

  • Bayraktar E, Young VR (2008) Minimizing the probability of ruin when consumption is ratcheted. N Am Actuar J 12(4):428–442

    Article  MathSciNet  Google Scholar 

  • Browne S (1995) Optimal investment policies for a firm with a random risk process: exponential utility and minimizing the probability of ruin. Math Oper Res 20(4):937–958

    Article  MathSciNet  MATH  Google Scholar 

  • Collamore JF (2009) Random recurrence equations and ruin in a Markov-dependent stochastic economic environment. Ann Appl Probab 19(4):1404–1458

    Article  MathSciNet  MATH  Google Scholar 

  • Delong L (2005) Optimal investment strategy for a non-life insurance company: quadratic loss. Appl Math 32(3):263

    MathSciNet  MATH  Google Scholar 

  • Feller W (1950) An introduction to probability theory and its applications, vol I. Wiley, New York

    MATH  Google Scholar 

  • Frolova A, Kabanov Y, Pergamenshchikov S (2002) In the insurance business risky investments are dangerous. Financ Stoch 6(2):227–235

    Article  MathSciNet  MATH  Google Scholar 

  • Gaier J, Grandits P, Schachermayer W (2003) Asymptotic ruin probabilities and optimal investment. Ann Appl Probab 13(3):1054–1076

    Article  MathSciNet  MATH  Google Scholar 

  • Gerber HU (1979) An introduction to mathematical risk theory (No. 517/G36i)

  • Grandits P (2004) A Karamata-type theorem and ruin probabilities for an insurer investing proportionally in the stock market. Insur Math Econ 34(2):297–305

    Article  MathSciNet  MATH  Google Scholar 

  • Hipp C, Plum M (2000) Optimal investment for insurers. Insur Math Econ 27(2):215–228

    Article  MathSciNet  MATH  Google Scholar 

  • Kostadinova R (2007) Optimal investment for insurers when the stock price follows an exponential Lévy process. Insur Math Econ 41(2):250–263

    Article  MathSciNet  MATH  Google Scholar 

  • Liu CS, Yang H (2004) Optimal investment for an insurer to minimize its probability of ruin. N Am Actuar J 8(2):11–31

    Article  MathSciNet  MATH  Google Scholar 

  • Lundberg F (1903) Approximerad Framställning av Sannolikhetsfunktionen. Återförsäkring av Kollektivrisker. Akad. Afhandling, Almqvist och Wiksell, Uppsala

    Google Scholar 

  • Nyrhinen H (2001) Finite and infinite time ruin probabilities in a stochastic economic environment. Stoch Process Appl 92(2):265–285

    Article  MathSciNet  MATH  Google Scholar 

  • Osu BO, Ihedioha SA, Adindu-Dick JI (2014) On the survival of insurance company™ investment with consumption under power and exponential utility functions. Am J Appl Math 2(1):8–13

    Article  Google Scholar 

  • Pergamenshchikov S, Zeitouny O (2006) Ruin probability in the presence of risky investments. Stoch Process Appl 116(2):267–278

    Article  MathSciNet  MATH  Google Scholar 

  • Wei L (2009) Ruin probability of the renewal model with risky investment and large claims. Sci China, Ser A Math 52(7):1539–1545

    Article  MathSciNet  MATH  Google Scholar 

  • Young VR (2004) Optimal investment strategy to minimize the probability of lifetime ruin. N Am Actuar J 8(4):106–126

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

The support of Higher Education Commission of Islamabad is gratefully acknowledged. We also acknowledge the fruitful comments of the anonymous referees.

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Correspondence to Sultan Hussain.

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Hussain, S., Parvez, A. Wealth Investment Strategies for Insurance Companies and the Probability of Ruin. Iran J Sci Technol Trans Sci 42, 1555–1561 (2018). https://doi.org/10.1007/s40995-017-0166-4

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  • DOI: https://doi.org/10.1007/s40995-017-0166-4

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