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Crossing Probabilities for Diffusion Processes with Piecewise Continuous Boundaries

Liqun Wang () and Klaus Pötzelberger ()
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Klaus Pötzelberger: University of Economics and Business Administration Vienna

Methodology and Computing in Applied Probability, 2007, vol. 9, issue 1, 21-40

Abstract: Abstract We propose an approach to compute the boundary crossing probabilities for a class of diffusion processes which can be expressed as piecewise monotone (not necessarily one-to-one) functionals of a standard Brownian motion. This class includes many interesting processes in real applications, e.g., Ornstein–Uhlenbeck, growth processes and geometric Brownian motion with time dependent drift. This method applies to both one-sided and two-sided general nonlinear boundaries, which may be discontinuous. Using this approach explicit formulas for boundary crossing probabilities for certain nonlinear boundaries are obtained, which are useful in evaluation and comparison of various computational algorithms. Moreover, numerical computation can be easily done by Monte Carlo integration and the approximation errors for general boundaries are automatically calculated. Some numerical examples are presented.

Keywords: Boundary crossing probabilities; Brownian motion; Diffusion process; First hitting time; First passage time; Wiener process; Primary 60J60; 60J70; Secondary 60J25; 60G40; 65C05 (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1007/s11009-006-9002-6

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