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Some applications and methods of large deviations in finance and insurance

  • Huyen Pham

    (PMA)

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    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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    File URL: http://arxiv.org/pdf/math/0702473
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    Paper provided by arXiv.org in its series Papers with number math/0702473.

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    Date of creation: Feb 2007
    Date of revision: Feb 2007
    Handle: RePEc:arx:papers:math/0702473
    Contact details of provider: Web page: http://arxiv.org/

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    1. Asmussen, Søren & Klüppelberg, Claudia, 1996. "Large deviations results for subexponential tails, with applications to insurance risk," Stochastic Processes and their Applications, Elsevier, vol. 64(1), pages 103-125, November.
    2. Sornette, Didier, 1998. "Large deviations and portfolio optimization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 256(1), pages 251-283.
    3. Paolo Baldi & Lucia Caramellino & Maria Gabriella Iovino, 1999. "Pricing General Barrier Options: A Numerical Approach Using Sharp Large Deviations," Mathematical Finance, Wiley Blackwell, vol. 9(4), pages 293-321.
    4. Gobet, Emmanuel, 2000. "Weak approximation of killed diffusion using Euler schemes," Stochastic Processes and their Applications, Elsevier, vol. 87(2), pages 167-197, June.
    5. Paul Glasserman & Jingyi Li, 2005. "Importance Sampling for Portfolio Credit Risk," Management Science, INFORMS, vol. 51(11), pages 1643-1656, November.
    6. Noah Williams, 2003. "Small Noise Asymptotics for a Stochastic Growth Model," NBER Working Papers 10194, National Bureau of Economic Research, Inc.
    7. Stutzer, Michael, 2003. "Portfolio choice with endogenous utility: a large deviations approach," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 365-386.
    8. Didier Sornette, 1998. "Large deviations and portfolio optimization," Papers cond-mat/9802059, arXiv.org, revised Jun 1998.
    9. Amir Dembo & Jean-Deominique Deuschel & Darrell Duffie, 2002. "Large Portfolio Losses," NBER Working Papers 9177, National Bureau of Economic Research, Inc.
    10. 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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