Computational Methods in Finance Related to Distributions with Known Marginals

Model uncertainty and the dependence structures of various risk factors are important components of measuring and managing financial risk, such as market, credit and operational risks. In this thesis we provide a systematic investigation into these issues by studying their impacts on Credit Value Adjustment (CVA), Counterparty Credit Risk (CCR), and estimating Value-at-Risk for a portfolio of financial instruments. In particular we address the numerical issues of finding an unknown (worst-case) copula that ties marginal distributions of risk factors together given partial information about them