Salisbury, ThomasKuznetsov, Alexey2018-05-282018-05-282017-11-202018-05-28http://hdl.handle.net/10315/34554A new class of exponential functionals arises when pricing certain equity-linked insurance products.We study the distribution of these exponential functionals using tools from Probability and Complex Analysis. In the case of the Kou process we obtain an explicit formula for the probability density function of the exponential functional and we apply this result to pricing equity-linked insurance products. As a by-product of this research we have also derived a new class of duality relations for hypergeometric functions. In the second part of the thesis, we study correlation uncertainty in Credit Risk. The goal is to price analogues of first-to-default options under the assumption that the assets follow correlated stochastic processes with known marginal distributions and unknown dependence structure. We solve this problem using tools from Stochastic Analysis and Optimal Control Theory. We provide explicit solutions in some specific examples and numerical approximations in the more general case.enAuthor owns copyright, except where explicitly noted. Please contact the author directly with licensing requests.FinanceElectronic Thesis or Dissertation2018-05-28Levy processesKou processesGeneral exponential functionalSkew Brownian motionAsymmetric local timeMellin transformBarnes- G functionVariable annuity guaranteed benefitsFirst to defaultUncertain correlationUnknown dependence structureOptimal control theory.