Classical finance models reply on a probabilistic framework where the laws of risky assets are known. However, this assumption is restrictive in practical applications, and it has become clear that model uncertainty, i.e., the risk of using wrong models, cannot be ignored. In practice, such model failures will usually lead to huge losses. For instance, in 1998, Nat West Capital Markets announced a $50 million loss because of a mispriced portfolio on interest rate options.
Recently, dealing with model uncertainty is an active research area of mathematical finance, because the ability to achieve more reliable tools with respect to model errors. In this project, the student will
1) Develop mathematical tools for the problems of finding robust prices and robust hedging strategies in more realistic settings, for example, where stocks are paying dividends or traded under constraints.
2) Develop numerical methods to solve these problems.