2012/05/03 by Andreas E. Kyprianou, Kyprianou, Andreas E., Juan Carlos Pardo +3
Decision Sciences · Economics, Econometrics and Finance · #60J99 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1205.0756
openalex publication_date 2012/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A refracted Lévy process is a Lévy process whose dynamics change by subtracting off a fixed linear drift (of suitable size) whenever the aggregate process is above a pre-specified level. More precisely, whenever it exists, a refracted Lévy process is described by the unique strong solution to the stochastic differential equation \ud Ut=-δ1_\Utgt;b\\ud t +\ud Xt, where X=(Xt, t≥ 0) is a Lévy process with law \p and b,δ∈ \R such that the resulting process U may visit the half line (b,∞) with positive probability. In this paper, we consider the case that X is spectrally negative and establish a number of identities for the following functionals \[ ∫0^∞1_\Ut<b> a\ and ρ-c=inf\t≥ 0: Ut< c\ for c<b></b></b>