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Continuity Theorems in Boundary Crossing Problems for Diffusion Processes

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Contemporary Quantitative Finance

Abstract

Computing the probability for a given diffusion process to stay under a particular boundary is crucial in many important applications including pricing financial barrier options and defaultable bonds. It is a rather tedious task that, in the general case, requires the use of some approximation methodology. One possible approach to this problem is to approximate given (general curvilinear) boundaries with some other boundaries of a form enabling one to relatively easily compute the boundary crossing probability. We discuss results on the accuracy of such approximations for both the Brownian motion process and general time-homogeneous diffusions and also some contiguous topics.

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Author information

Authors and Affiliations

  1. Dept. of Mathematics and Statistics, Univ. of Melbourne, Parkville, 3010, Australia

    Konstantin A. Borovkov & Andrew N. Downes

  2. Dept. of Mathematical Sciences, The University of Technology, PO Box 123, Broadway, Sydney, NSW, 2007, Australia

    Alexander A. Novikov

Authors
  1. Konstantin A. Borovkov
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  2. Andrew N. Downes
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  3. Alexander A. Novikov
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Corresponding author

Correspondence to Alexander A. Novikov .

Editor information

Editors and Affiliations

  1. School of Finance and Economics Department of Mathematical Sciences, The University of Technology, Sydney, P.O. Box 123, Broadway 2007, NSW, Australia

    Carl Chiarella  & Alexander Novikov  & 

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Borovkov, K.A., Downes, A.N., Novikov, A.A. (2010). Continuity Theorems in Boundary Crossing Problems for Diffusion Processes. In: Chiarella, C., Novikov, A. (eds) Contemporary Quantitative Finance. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03479-4_17

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