On exit times of Levy-driven Ornstein–Uhlenbeck processes
Copyright policy )On exit times of Levy-driven Ornstein–Uhlenbeck processes
We prove two martingale identities which involve exit times of Levy-driven Ornstein--Uhlenbeck processes. Using these identities we find an explicit formula for the Laplace transform of the exit time under the assumption that positive jumps of the Levy process are exponentially distributed.
12 pages
- University of Melbourne Australia
- University of Technology Sydney Australia
Stopping times; optimal stopping problems; gambling theory, 60G44; 60F05, Lévy-driven Ornstein-Uhlenbeck processes, Laplace transform, Probability (math.PR), Martingales with continuous parameter, exit times, Processes with independent increments; Lévy processes, Characteristic functions; other transforms, 60F05, FOS: Mathematics, 60G44, Jump processes, Mathematics - Probability
Stopping times; optimal stopping problems; gambling theory, 60G44; 60F05, Lévy-driven Ornstein-Uhlenbeck processes, Laplace transform, Probability (math.PR), Martingales with continuous parameter, exit times, Processes with independent increments; Lévy processes, Characteristic functions; other transforms, 60F05, FOS: Mathematics, 60G44, Jump processes, Mathematics - Probability
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