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A Hybrid Estimate for the Finite-Time Ruin Probability in a Bivariate Autoregressive Risk Model with Application to Portfolio Optimization

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  • Qihe Tang
  • Zhongyi Yuan

Abstract

Consider a discrete-time risk model in which the insurer is allowed to invest a proportion of its wealth in a risky stock and keep the rest in a risk-free bond. Assume that the claim amounts within individual periods follow an autoregressive process with heavy-tailed innovations and that the log-returns of the stock follow another auto regressive process, independent of the former one. We derive an asymptotic formula for the finite-time ruin probability and propose a hybrid method, combining simulation with asymptotics, to compute this ruin probability more efficiently. As an application, we consider a portfolio optimization problem in which we determine the proportion invested in the risky stock that maximizes the expected terminal wealth subject to a constraint on the ruin probability.

Suggested Citation

  • Qihe Tang & Zhongyi Yuan, 2012. "A Hybrid Estimate for the Finite-Time Ruin Probability in a Bivariate Autoregressive Risk Model with Application to Portfolio Optimization," North American Actuarial Journal, Taylor & Francis Journals, vol. 16(3), pages 378-397.
    • Handle: RePEc:taf:uaajxx:v:16:y:2012:i:3:p:378-397
    DOI: 10.1080/10920277.2012.10590648
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    Cited by:

    1. Yiqing Chen & Jiajun Liu & Yang Yang, 2023. "Ruin under Light-Tailed or Moderately Heavy-Tailed Insurance Risks Interplayed with Financial Risks," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-26, March.
    2. Fu, Ke-Ang & Ng, Cheuk Yin Andrew, 2017. "Uniform asymptotics for the ruin probabilities of a two-dimensional renewal risk model with dependent claims and risky investments," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 227-235.
    3. Jing Liu & Huan Zhang, 2017. "Asymptotic Estimates for the One-Year Ruin Probability under Risky Investments," Risks, MDPI, vol. 5(2), pages 1-11, May.
    4. Jaunė, Eglė & Šiaulys, Jonas, 2022. "Asymptotic risk decomposition for regularly varying distributions with tail dependence," Applied Mathematics and Computation, Elsevier, vol. 427(C).
    5. Rafik Nazarian & Ashkan Amiri, 2014. "Asymmetry of the Oil Price Pass Through to Inflation in Iran," International Journal of Energy Economics and Policy, Econjournals, vol. 4(3), pages 457-464.

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