In financial markets, transaction costs and other types of frictions play a critical role. In particular, they prevent the use of hedging strategies computed for ideal trading conditions. Still, it is desirable to use these portfolios by appropriately modifying them. These constructions share certain common general principals but they also depend on the structure of the specific problems. In addition to their apparent importance in applications, they also offer exciting new problems in stochastic optimal control.
In this talk, after outlining two general results, I will consider the problem of hedging leveraged exchange-traded funds (LETF). Exchange traded funds (ETF) and LETFs are recent financial products that are rapidly gaining a large market size. LETFs promise to provide a certain multiple of the daily return of the underlying ETF. The matching is done daily and is very different than matching for longer periods. This need of frequent portfolio balancing introduces difficulties. Using the general approaches, I describe a model that allows for frictions. After describing the theoretical results, I will conclude with numerical experiments.