In this thesis, we consider computational methods of finding exit probabilities for a class of multivariate stochastic
processes. While there is an abundance of results for one-dimensional processes, for multivariate processes one has to
rely on approximations or simulation methods. We adopt a Large Deviations approach in order to estimate barrier crossing probabilities of a multivariate Brownian Bridge. We use this approach in conjunction with numerical techniques to propose an efficient method of obtaining barrier crossing probabilities of a
multivariate Brownian motion. Using numerical examples, we demonstrate that our method works better than other existing
methods. We present applications of the proposed method in addressing problems in finance such as estimating default
probabilities of several credit risky entities and pricing credit default swaps. We also extend our computational method to
efficiently estimate a barrier crossing probability of a sum of Geometric Brownian motions. This allows us to perform a portfolio selection by maximizing a path-dependent utility function.
| Identifer | oai:union.ndltd.org:WATERLOO/oai:uwspace.uwaterloo.ca:10012/3202 |
| Date | 15 August 2007 |
| Creators | Huh, Joonghee |
| Source Sets | University of Waterloo Electronic Theses Repository |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
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