We prove large deviation principles for two versions of fractional Poisson processes: the main version is a renewal process, the alternative version is a weighted Poisson process. We also present asymptotic results for the ruin probabilities of an insurance model with a fractional Poisson claim...

In this article, we consider the problem of the minimal entropy martingale measure of a jump process influenced by jump times. The minimal entropy martingale measure of the price process is given out by the exponential martingale method, and the expression of the corresponding relative entropy...

In this article, we establish several deviations for convex and coherent entropic risk measures. Firstly, we provide several deviations for the two risk measures with respect to relative entropy. Secondly, we provide several deviations for the two risk measures with respect to parameters....