This paper studies regularity properties of the value function for an infinite-horizon discounted cost impulse control problem, where the underlying controlled process is a multidimensional jump diffusion with possibly ‘infinite-activity’ jumps. Surprisingly, despite these jumps, we obtain the same degree of regularity as for the diffusion case, at least when the jump satisfies certain integrab...

An alternative option pricing model is proposed, in which the asset prices follow the jump-diffusion and exhibits mean reversion. The stochastic volatility follows the jump-diffusion with mean reversion. We find a formulation for the European-style option in terms of characteristic functions.

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.

This note uses sum of squares (SOS) relaxation to solve stochastic reachability problems for jump-diffusion processes. The main result is a polynomial characterization of the infinitesimal generator for the solution of a jump-diffusion process’ boundary value problem, thereby enabling one to compute a bound on the probability of reaching a target set in finite time using SOS optimization.

Abstract This paper is a contribution to special issue on Data Science: Present and Future , because the main topic has been will be in an active area of contemporary data science. High-frequency financial are commonly available by now. To estimate Brownian jump functionals from high-frequency under market micro-structure noise, we introduce new local estimation method integrated volatility hig...