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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.

Suggested Citation

  • 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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    File URL: http://arxiv.org/pdf/math/0702473
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    References listed on IDEAS

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    1. Williams, Noah, 2004. "Small noise asymptotics for a stochastic growth model," Journal of Economic Theory, Elsevier, vol. 119(2), pages 271-298, December.
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    7. Paul Glasserman & Jingyi Li, 2005. "Importance Sampling for Portfolio Credit Risk," Management Science, INFORMS, vol. 51(11), pages 1643-1656, November.
    8. Amir Dembo & Jean-Dominique Deuschel & Darrell Duffie, 2004. "Large portfolio losses," Finance and Stochastics, Springer, vol. 8(1), pages 3-16, January.
    9. Stutzer, Michael, 2003. "Portfolio choice with endogenous utility: a large deviations approach," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 365-386.
    10. Arouna Bouhari, 2004. "Adaptative Monte Carlo Method, A Variance Reduction Technique," Monte Carlo Methods and Applications, De Gruyter, vol. 10(1), pages 1-24, March.
    11. Paul Glasserman & Philip Heidelberger & Perwez Shahabuddin, 1999. "Asymptotically Optimal Importance Sampling and Stratification for Pricing Path-Dependent Options," Mathematical Finance, Wiley Blackwell, vol. 9(2), pages 117-152.
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    Cited by:

    1. repec:eee:spapps:v:127:y:2017:i:9:p:2926-2960 is not listed on IDEAS
    2. 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.
    3. 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.
    4. 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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