2021/05/28 by Christophe Profeta, Profeta, Christophe
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #60G40 #60J60 #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2105.13706
openalex publication_date 2021/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We compute the joint distribution of the first times a linear diffusion makes an excursion longer than some given duration above (resp. below) some fixed level. In the literature, such stopping times have been introduced and studied in the framework of Parisian barrier options, mainly in the case of Brownian motion with drift. We also exhibit several independence properties, and provide some formulae for the associated ruin probabilities.