Type of Document	Dissertation
Author	Shah, Manan
Author's Email Address	manyshah@gmail.com
URN	etd-07102008-162540
Title	Quasi-Monte Carlo and Genetic Algorithms with Applications to Endogenous Mortgage Rate Computation
Degree	Doctor of Philosophy
Department	Mathematics, Department of
Advisory Committee	Advisor Name Title Dr. Alec Kercheval Committee Member Dr. Ashok Srinivasan Committee Member Dr. Bettye Anne Case Committee Member Dr. David Kopriva Committee Member Dr. Giray Okten Committee Member Dr. Steve Bellenot Committee Member Dr. Warren Nichols Committee Member Dr. Yevgeny Goncharov Committee Member
Keywords	Halton Sequence Discrepancy Digit Permutations MOATS Citigroup
Date of Defense	2008-04-21
Availability	unrestricted
Abstract In this dissertation, we introduce a genetic algorithm approach to estimate the star discrepancy of a point set. This algorithm allows for the estimation of the star discrepancy in dimensions larger than seven, something that could not be done adequately by other existing methods. Then, we introduce a class of random digit-permutations for the Halton sequence and show that these permutations yield comparable or better results than their deterministic counterparts in any number of dimensions for the test problems considered. Next, we use randomized quasi-Monte Carlo methods to numerically solve a one-factor mortgage model expressed as a stochastic fixed-point problem. Finally, we show that this mortgage model coincides with and is computationally faster than Citigroup's MOATS model, which is based on a binomial tree approach.
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