DEVIATION INEQUALITIES FOR EXPONENTIAL JUMP-DIFFUSION PROCESSES

B. LAQUERRIÈRE AND N. PRIVAULT

Theory of Stochastic Processes

Vol.16 (32), no.1, 2010, pp.67-72


In this note we obtain deviation inequalities for the law of exponential jump-diffusion processes at a fixed time. Our method relies on convex concentration inequalities obtained by forward/backward stochastic calculus. In the pure jump and pure diffusion cases, it also improves on classical results obtained by direct application of Gaussian and Poisson bounds.