The theory of large deviations deals with "rare" events, whose probability decreases exponentially w.r.t. some parameter. A classical example are sample means which are "far" from the true expectation inspite of a "large" sample size. We will cover the following subjects from the general theory: Cramer's theorem, Gärtner-Ellis theorem, general LDP (large deviation principle), Varadhan's lemma, and fundamentals of the Freidlin-Ventzell theory about sample path large deviations. Applications: Option pricing by Monte Carlo (importance sampling), large losses in credit risk management, asymptotics of option prices for short maturities.
I will try to adjust the proportion of theory vs. financial applications to the background and interests of the participants.
Introduction:
den Hollander: Large deviations, American Mathematical Society, 2008
Advanced books:
Dembo, Zeitouni: Large deviations techniques and applications, Springer 1998
Dupuis, Ellis: A weak convergence approach to the theory of large deviations, Wiley 1997
Applications:
Pham: Some applications and methods of large deviations in finance and insurance, Lecture Notes in Math. 1919, Springer, Berlin, 2007
https://doi.org/10.1007/978-3-540-73327-0_5
Boyle, Feng, Tian: Large Deviation Techniques and Financial Applications, Handbooks in Operations Research and Management Science, vol. 15, 2007, 971-1000
http://dx.doi.org/10.1016/S0927-0507(07)15024-6
Friz et al. (ed.): Large deviations and asymptotic methods in finance, Springer 2015
