With model uncertainty characterized by a convex, possibly non-dominated set of probability measures, the investor minimizes the cost of hedging a path dependent contingent claim with given expected success ratio, in a discrete-time, semi-static market of stocks and options. Based on duality...

A hedge fund manager invests the fund in a constant investment opportunity, and receives high-water mark fees when the fund reaches a new maximum relative to a stochastic benchmark, aiming to maximize the expected power utility from fees in the long run. The manager's optimal portfolio includes...

In the high-frequency limit, conditional expected increments of fractional Brownian motion converge to a white noise, shedding their dependence on the path history and the forecasting horizon, and making dynamic optimization problems tractable. We find an explicit formula for locally...