Computational biology

Hierarchical Approximation Methods for Option Pricing and Stochastic Reaction Networks

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KAUST

In biochemically reactive systems with small copy numbers of one or more reactant molecules, stochastic effects dominate the dynamics. In the first part of this thesis, we design novel efficient simulation techniques, based on multilevel Monte Carlo methods and importance sampling, for a reliable and fast estimation of various statistical quantities for stochastic biological and chemical systems under the framework of Stochastic Reaction Networks (SRNs). In the second part of this thesis, we design novel numerical methods for pricing financial derivatives. Option pricing is usually challenging due to a combination of two complications: 1) The high dimensionality of the input space, and 2) The low regularity of the integrand on the input parameters. We address these challenges by using different techniques for smoothing the integrand to uncover the available regularity and improve quadrature methods' convergence behavior. We develop different ways of smoothing that depend on the characteristics of the problem at hand. Then, we approximate the resulting integrals using hierarchical quadrature methods combined with Brownian bridge construction and Richardson extrapolation.

Chiheb Ben Hammouda

Chiheb Ben Hammouda is a Ph.D. candidate at Stochastic Numerics Research Group (STOCHNUM) under the supervision of Professor Raul F. Tempone at King Abdullah University of Science and Technology (KAUST). Prior to joining Ph.D., Chiheb obtained a Master's degree in Applied Mathematics and Computational Sciences from KAUST, and a Bachelor's degree in multidisciplinary engineering from Ecole Polytechnique de Tunisie, Tunisia. Research Interests Chiheb's research interests include Stochastic modeling, Numerical simulation and analysis, Quantitative finance in particular option pricing, Stochastic