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Ruin probabilities and optimal investment when the stock price follows an exponential Lévy process

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  • Li, Ping
  • Zhao, Wu
  • Zhou, Wei

Abstract

This paper investigates the infinite and finite time ruin probability under the condition that the company is allowed to invest a certain amount of money in some stock market, and the remaining reserve in the bond with constant interest force. The total insurance claim amount is modeled by a compound Poisson process and the price of the risky asset follows a general exponential Lévy process. Exponential type upper bounds for the ultimate ruin probability are derived when the investment is a fixed constant, which can be calculated explicitly. This constant investment strategy yields the optimal asymptotic decay of the ruin probability under some mild assumptions. Finally, we provide an approximation of the optimal investment strategy, which maximizes the expected wealth of the insurance company under a risk constraint on the Value-at-Risk.

Suggested Citation

  • Li, Ping & Zhao, Wu & Zhou, Wei, 2015. "Ruin probabilities and optimal investment when the stock price follows an exponential Lévy process," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 1030-1045.
    • Handle: RePEc:eee:apmaco:v:259:y:2015:i:c:p:1030-1045
    DOI: 10.1016/j.amc.2014.12.042
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    Cited by:

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    2. Jorge Ignacio Gonz'alez C'azares & Aleksandar Mijatovi'c, 2021. "Monte Carlo algorithm for the extrema of tempered stable processes," Papers 2103.15310, arXiv.org, revised Dec 2022.
    3. Yanfei Bai & Zhongbao Zhou & Helu Xiao & Rui Gao & Feimin Zhong, 2019. "A hybrid stochastic differential reinsurance and investment game with bounded memory," Papers 1910.09834, arXiv.org.
    4. Bai, Yanfei & Zhou, Zhongbao & Xiao, Helu & Gao, Rui & Zhong, Feimin, 2022. "A hybrid stochastic differential reinsurance and investment game with bounded memory," European Journal of Operational Research, Elsevier, vol. 296(2), pages 717-737.
    5. Jorge Gonz'alez C'azares & Aleksandar Mijatovi'c, 2020. "Simulation of the drawdown and its duration in L\'{e}vy models via stick-breaking Gaussian approximation," Papers 2011.06618, arXiv.org, revised Mar 2021.

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