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Some applications and methods of large deviations in finance and insurance

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  • Huyen Pham

    (PMA)

Abstract

In these notes, we present some methods and applications of large deviations to finance and insurance. We begin with the classical ruin problem related to the Cramer's theorem and give en extension to an insurance model with investment in stock market. We then describe how large deviation approximation and importance sampling are used in rare event simulation for option pricing. We finally focus on large deviations methods in risk management for the estimation of large portfolio losses in credit risk and portfolio performance in market investment.

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  • Huyen Pham, 2007. "Some applications and methods of large deviations in finance and insurance," Papers math/0702473, arXiv.org, revised Feb 2007.
    • Handle: RePEc:arx:papers:math/0702473
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Jacquier, Antoine & Roome, Patrick, 2016. "Large-maturity regimes of the Heston forward smile," Stochastic Processes and their Applications, Elsevier, vol. 126(4), pages 1087-1123.
    2. Spiliopoulos, Konstantinos & Sowers, Richard B., 2011. "Recovery rates in investment-grade pools of credit assets: A large deviations analysis," Stochastic Processes and their Applications, Elsevier, vol. 121(12), pages 2861-2898.
    3. Djellout, Hacène & Guillin, Arnaud & Samoura, Yacouba, 2017. "Estimation of the realized (co-)volatility vector: Large deviations approach," Stochastic Processes and their Applications, Elsevier, vol. 127(9), pages 2926-2960.
    4. Dan Pirjol & Xiaoyu Wang & Lingjiong Zhu, 2024. "Short-maturity asymptotics for VIX and European options in local-stochastic volatility models," Papers 2407.16813, arXiv.org.
    5. Youngha Cho & Soosung Hwang & Steve Satchell, 2012. "The Optimal Mortgage Loan Portfolio in UK Regional Residential Real Estate," The Journal of Real Estate Finance and Economics, Springer, vol. 45(3), pages 645-677, October.
    6. Dai Pra, Paolo & Tolotti, Marco, 2009. "Heterogeneous credit portfolios and the dynamics of the aggregate losses," Stochastic Processes and their Applications, Elsevier, vol. 119(9), pages 2913-2944, September.
    7. Dan Pirjol & Lingjiong Zhu, 2024. "Short-maturity asymptotics for option prices with interest rates effects," Papers 2402.14161, arXiv.org.
    8. Erhan Bayraktar & Asaf Cohen, 2015. "Risk Sensitive Control of the Lifetime Ruin Problem," Papers 1503.05769, arXiv.org, revised Jul 2016.
    9. Konstantinos Spiliopoulos & Richard B. Sowers, 2010. "Recovery Rates in investment-grade pools of credit assets: A large deviations analysis," Papers 1006.2711, arXiv.org, revised Aug 2011.
    10. Paolo Dai Pra & Wolfgang J. Runggaldier & Elena Sartori & Marco Tolotti, 2007. "Large portfolio losses: A dynamic contagion model," Papers 0704.1348, arXiv.org, revised Mar 2009.
    11. Aur'elien Alfonsi & David Krief & Peter Tankov, 2018. "Long-time large deviations for the multi-asset Wishart stochastic volatility model and option pricing," Papers 1806.06883, arXiv.org.
    12. Pierre-Loic M'eliot & Ashkan Nikeghbali & Gabriele Visentin, 2022. "Mod-Poisson approximation schemes: Applications to credit risk," Papers 2211.04436, arXiv.org.
    13. Robertson, Scott, 2010. "Sample path Large Deviations and optimal importance sampling for stochastic volatility models," Stochastic Processes and their Applications, Elsevier, vol. 120(1), pages 66-83, January.

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