Computational and statistical topics from modern finance

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Modern financial instruments designed as contingent claims on equities, currency rates, and other securities have achieved enormous success in global financial markets. They have provided institutional investors with new vehicles to meet their diverse financial needs. The success of these instruments can largely be attributed to mathematical models that have given foundations for their pricing. In the proposed research, I will address some computational and statistical issues related to risk management of such products. In particular, I will consider models that provide more realistic descriptions of different risk factors than the existing ones. They are based on jump and Levy processes, and often are characterized by means of a transformation only. This makes classical methods based on likelihood functions infeasible. I will focus on the problems of dynamic portfolio selection and the pricing of American style contracts contingent on several assets. The statistical issues that I will study include estimation and filtering for models involving jump and Levy processes.