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Estimating Finite-Time Ruin Probability of Surplus with Long Memory via Malliavin Calculus

In: Research Papers in Statistical Inference for Time Series and Related Models

Author

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  • Shota Nakamura

    (Waseda University)

  • Yasutaka Shimizu

    (Waseda University)

Abstract

We consider a surplus process of a drifted fractional Brownian motion with the Hurst index $$H>1/2$$ H > 1 / 2 , which appears as a functional limit of drifted compound Poisson risk models with correlated claims. This is a kind of representation of a surplus with a long memory. Our interest is to construct confidence intervals of the ruin probability of the surplus when the volatility parameter is unknown. We obtain the derivative of the ruin probability w.r.t. the volatility parameter via the Malliavin calculus, and apply the delta method to identify the asymptotic distribution of an estimated ruin probability.

Suggested Citation

  • Shota Nakamura & Yasutaka Shimizu, 2023. "Estimating Finite-Time Ruin Probability of Surplus with Long Memory via Malliavin Calculus," Springer Books, in: Yan Liu & Junichi Hirukawa & Yoshihide Kakizawa (ed.), Research Papers in Statistical Inference for Time Series and Related Models, chapter 0, pages 455-474, Springer.
    • Handle: RePEc:spr:sprchp:978-981-99-0803-5_20
    DOI: 10.1007/978-981-99-0803-5_20
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