First-passage problems for diffusion processes with state-dependent jumps. Issue 9 (25th March 2022) - Lefebvre, Mario
Abstract: Let X ( t ) be a time-homogeneous jump-diffusion process. We assume that the jump size depends on the value of X ( t ). We obtain analytical results for the moments of T ( x ) and of X ( T ( x ) ), where T ( x ) is the first time that the process leaves the interval ( a, b ). We also compute P [ X ( T ( x ) ) ≤ a ] . These results have applications in financial mathematics.