Sensitivity Problems for Boundary Crossing
Konstantin Borovkov1, Andrew N. Downes1, Alexander Novikov2
1Department of Mathematics and Statistics, The University of Melbourne, VIC, Australia; 2Department of Mathematical Sciences, The University of Technology, Sydney, Sydney, NSW, Australia

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. 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. In our talk, we discuss the problem of the sensitivity of the boundary crossing probabilities with respect to small perturbations of the boundaries, both in the case of the Brownian motion process and that of general time-homogeneous diffusions.

Keywords: Diffusion process; Boundry crossing; Sensititivy; Approximation rate

Biography: Konstantin Borovkov is Professor of Mathematics and Statistics at the University of Melbourne, Australia. After graduating from the Novosibirsk State University, he earned his PhD in Probability and Mathematical Statistics from Steklov Mathematical Institute of the Academy of Sciences of the USSR in 1982, and then DrSci in 1994. Borovkov's research spanned a range of areas in probability and statistics, and he authored a graduate level text on stochastic modelling (World Scientific, 2003) and co-authored a monograph of large deviation probabilities (Cambridge University Press, 2008). Prior to coming to Melbourne in 1995, he had worked at Steklov Mathematical Institute and in 1991-2 was a Humboldt Research Fellow at Carl von Ossietzky University of Oldenburg, Germany.