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Some applications and methods of large deviations in finance and insurance

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Author Info
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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File URL: http://arxiv.org/abs/math/0702473
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File URL: http://arxiv.org/pdf/math/0702473
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Paper provided by arXiv.org in its series Quantitative Finance 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

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  1. Amir Dembo & Jean-Dominique Deuschel & Darrell Duffie, 2004. "Large portfolio losses," Finance and Stochastics, Springer, vol. 8(1), pages 3-16, January. [Downloadable!] (restricted)
  2. Williams, Noah, 2004. "Small noise asymptotics for a stochastic growth model," Journal of Economic Theory, Elsevier, vol. 119(2), pages 271-298, December. [Downloadable!] (restricted)
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  3. Stutzer, Michael, 2003. "Portfolio choice with endogenous utility: a large deviations approach," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 365-386. [Downloadable!] (restricted)
  4. Didier Sornette, 1998. "Large deviations and portfolio optimization," Quantitative Finance Papers cond-mat/9802059, arXiv.org, revised Jun 1998. [Downloadable!]
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