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Conditional Monte Carlo for sums, with applications to insurance and finance

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  • Asmussen, Søren

Abstract

Conditional Monte Carlo replaces a naive estimate Z of a number z by its conditional expectation given a suitable piece of information. It always reduces variance and its traditional applications are in that vein. We survey here other potential uses such as density estimation and calculations for Value-at-Risk and/or expected shortfall, going in part into the implementation in various copula structures. Also the interplay between these different aspects comes into play.

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  • Asmussen, Søren, 2018. "Conditional Monte Carlo for sums, with applications to insurance and finance," Annals of Actuarial Science, Cambridge University Press, vol. 12(2), pages 455-478, September.
    • Handle: RePEc:cup:anacsi:v:12:y:2018:i:02:p:455-478_00
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    Cited by:

    1. Kemal Dinçer Dingeç & Wolfgang Hörmann, 2022. "Efficient Algorithms for Tail Probabilities of Exchangeable Lognormal Sums," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 2093-2121, September.
    2. Zdravko I. Botev & Robert Salomone & Daniel Mackinlay, 2019. "Fast and accurate computation of the distribution of sums of dependent log-normals," Annals of Operations Research, Springer, vol. 280(1), pages 19-46, September.
    3. Hengxin Cui & Ken Seng Tan & Fan Yang, 2024. "Portfolio credit risk with Archimedean copulas: asymptotic analysis and efficient simulation," Papers 2411.06640, arXiv.org.
    4. Furman, Edward & Hackmann, Daniel & Kuznetsov, Alexey, 2020. "On log-normal convolutions: An analytical–numerical method with applications to economic capital determination," Insurance: Mathematics and Economics, Elsevier, vol. 90(C), pages 120-134.
    5. Qi Jun & Hasan Dinçer & Serhat Yüksel, 2021. "Stochastic hybrid decision‐making based on interval type 2 fuzzy sets for measuring the innovation capacities of financial institutions," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(1), pages 573-593, January.
    6. Pierre L’Ecuyer & Florian Puchhammer & Amal Ben Abdellah, 2022. "Monte Carlo and Quasi–Monte Carlo Density Estimation via Conditioning," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1729-1748, May.
    7. Boyle, Phelim & Jiang, Ruihong, 2023. "A note on portfolios of averages of lognormal variables," Insurance: Mathematics and Economics, Elsevier, vol. 112(C), pages 97-109.
    8. Laub, Patrick J. & Salomone, Robert & Botev, Zdravko I., 2019. "Monte Carlo estimation of the density of the sum of dependent random variables," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 161(C), pages 23-31.
    9. David Alaminos & M. Belén Salas & Manuel Á. Fernández-Gámez, 2023. "Quantum Monte Carlo simulations for estimating FOREX markets: a speculative attacks experience," Palgrave Communications, Palgrave Macmillan, vol. 10(1), pages 1-21, December.

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