Efficient and robust optimization approaches for financial applications

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Computationally challenging optimization problems are increasingly arising in the area of finance applications. I propose to work on two important examples.Firstly, in the insurance industry, risk management strategies under stochastic scenarios is an area of growing importance. The challenge here is twofold: how to properly formulate the problems in the language of optimization, and how to solve the resulting problems with an eye toward efficiency (computationally feasible!) and robustness. I will develop and investigate new (optimal) dynamic hedging strategies accounting for major complex risks including basis risk and surrender risk of segregated (variable annuity) insurance contracts.Secondly, I will examine the area of computing optimal investment strategies for portfolios involving hedge funds. This is a very challenging problem  for several reasons including scarcity of data and non-normality of the hedge fund return distributions. Traditional (equity-based) portfolio strategies are inappropriate. However, progress on this problem is urgently needed given the increased interest by both institutional and individual investors in diversifying their portfolios by investing in hedge funds. We will investigate robust, but computationally feasible, optimization approaches for this problem.