Fractal Fract, Vol. 7, Pages 152: First-Passage Times and Optimal Control of Integrated Jump-Diffusion Processes

Fractal Fract, Vol. 7, Pages 152: First-Passage Times and Optimal Control of Integrated Jump-Diffusion Processes

Fractal and Fractional doi: 10.3390/fractalfract7020152

Authors: Mario Lefebvre

Let Y(t) be a one-dimensional jump-diffusion process and X(t) be defined by dX(t)=ρ[X(t),Y(t)]dt, where ρ(·,·) is either a strictly positive or negative function. First-passage-time problems for the degenerate two-dimensional process (X(t),Y(t)) are considered in the case when the process leaves the continuation region at the latest at the moment of the first jump, and the problem of optimally controlling the process is treated as well. A particular problem, in which ρ[X(t),Y(t)]=Y(t)−X(t) and Y(t) is a standard Brownian motion with jumps, is solved explicitly.