Some applications and methods of large deviations in finance and insurance
AbstractIn 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by arXiv.org in its series Papers with number math/0702473.
Date of creation: Feb 2007
Date of revision: Feb 2007
Contact details of provider:
Web page: http://arxiv.org/
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Sornette, Didier, 1998. "Large deviations and portfolio optimization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 256(1), pages 251-283.
- Didier Sornette, 1998. "Large deviations and portfolio optimization," Papers cond-mat/9802059, arXiv.org, revised Jun 1998.
- Noah Williams, 2003.
"Small Noise Asymptotics for a Stochastic Growth Model,"
NBER Working Papers
10194, National Bureau of Economic Research, Inc.
- Williams, Noah, 2004. "Small noise asymptotics for a stochastic growth model," Journal of Economic Theory, Elsevier, vol. 119(2), pages 271-298, December.
- Noah Williams, 2003. "Small Noise Asymptotics for a Stochastic Growth Model," Computing in Economics and Finance 2003 262, Society for Computational Economics.
- Gobet, Emmanuel, 2000. "Weak approximation of killed diffusion using Euler schemes," Stochastic Processes and their Applications, Elsevier, vol. 87(2), pages 167-197, June.
- Amir Dembo & Jean-Dominique Deuschel & Darrell Duffie, 2004.
"Large portfolio losses,"
Finance and Stochastics,
Springer, vol. 8(1), pages 3-16, January.
- 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.
- 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.
- Stutzer, Michael, 2003. "Portfolio choice with endogenous utility: a large deviations approach," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 365-386.
- 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.
- 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.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators).
If references are entirely missing, you can add them using this form.