First-passage problems for diffusion processes with state-dependent jumps. Issue 9 (25th March 2022)

• Record Type: Journal Article
• Authors: Lefebvre, Mario
• Is Part Of: Communications in statistics. Volume 51:Issue 9(2022)
• Page Start: 2908
• Page End: 2918
• Publication Date: 2022-03-25
• Subjects: First-passage time -- Brownian motion -- Poisson process -- jump size -- differential-difference equation; 60J75 -- 60J60; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2020.1784433
• Languages: English
• ISSNs: 0361-0926

Abstract

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.