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A Saddlepoint Approximation to the Distribution of Inhomogeneous Discounted Compound Poisson Processes

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  • Riccardo Gatto

    (University of Bern)

Abstract

In this article we propose an accurate approximation to the distribution of the discounted total claim amount, where the individual claim amounts are independent and identically distributed and the number of claims over a specified period is governed by an inhomogeneous Poisson process. More precisely, we compute cumulant generating functions of such discounted total claim amounts under various intensity functions and individual claim amount distributions, and invert them by the saddlepoint approximation. We provide precise conditions under which the saddlepoint approximation holds. The resulting approximation is numerically accurate, computationally fast and hence more efficient than Monte Carlo simulation.

Suggested Citation

  • Riccardo Gatto, 2010. "A Saddlepoint Approximation to the Distribution of Inhomogeneous Discounted Compound Poisson Processes," Methodology and Computing in Applied Probability, Springer, vol. 12(3), pages 533-551, September.
    • Handle: RePEc:spr:metcap:v:12:y:2010:i:3:d:10.1007_s11009-008-9116-0
    DOI: 10.1007/s11009-008-9116-0
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    Cited by:

    1. Riccardo Gatto, 2012. "Saddlepoint Approximations to Tail Probabilities and Quantiles of Inhomogeneous Discounted Compound Poisson Processes with Periodic Intensity Functions," Methodology and Computing in Applied Probability, Springer, vol. 14(4), pages 1053-1074, December.
    2. Riccardo Gatto, 2019. "Saddlepoint Approximation for Data in Simplices: A Review with New Applications," Stats, MDPI, vol. 2(1), pages 1-27, February.
    3. Riccardo Gatto & Benjamin Baumgartner, 2014. "Value at Ruin and Tail Value at Ruin of the Compound Poisson Process with Diffusion and Efficient Computational Methods," Methodology and Computing in Applied Probability, Springer, vol. 16(3), pages 561-582, September.
    4. Gatto, Riccardo, 2015. "A logarithmic efficient estimator of the probability of ruin with recuperation for spectrally negative Lévy risk processes," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 177-184.

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