Extreme Deviations and Applications

6 The theory of large deviations and applications to statistical mechanics

Large Deviations with Diminishing Rate

The theory of large deviations for jump Markov processes has been generally proved only when jump rates are bounded below, away from zero [4, 8, 12]. Yet various applications of interest do not satisfy this condition. We describe several classes of models where jump rates diminish to zero in a Lipschitz continuous way. Under appropriate conditions, we prove that the sample path large deviations...

Large deviations for two scale chemical kinetic processes

We formulate the large deviations for a class of two scale chemical kinetic processes motivated from biological applications. The result is successfully applied to treat a genetic switching model with positive feedbacks. The corresponding Hamiltonian is convex with respect to the momentum variable as a by-product of the large deviation theory. This property ensures its superiority in the rare e...

Fe b 20 07 Some applications and methods of large deviations in finance and insurance ∗

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 focu...

Some applications and methods of large deviations in finance and insurance

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 focu...