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

Shota Nakamura () and Yasutaka Shimizu ()
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Shota Nakamura: Waseda University
Yasutaka Shimizu: Waseda University

Chapter Chapter 20 in Research Papers in Statistical Inference for Time Series and Related Models, 2023, pp 455-474 from Springer

Abstract: 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.

Keywords: Finite-time ruin probability; Long memory surplus; Fractional Brownian motion; Malliavin calculus; 60G22; 60H07; 62P05 (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-99-0803-5_20

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DOI: 10.1007/978-981-99-0803-5_20

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