Competition glider flying is a game of stochastic optimization, in which mathematics and quantitative strategies have historically played an important role. We address the problem of uncertain future atmospheric conditions by constructing a nonlinear Hamilton-Jacobi-Bellman equation for the...

Modern portfolio theory produces an optimal portfolio from estimates of expected returns and a covariance matrix. We present a method for portfolio optimization based on replacing expected returns with ordering information, that is, with information about the order of the expected returns. We...

Modern portfolio theory produces optimal portfolios from estimates of expected returns and a covariance matrix. Such optimal portfolios are efficient portfolios, that is they provide the maximum level of expected return for a given level of risk. We present a method for portfolio selection based...

We consider the problem of portfolio liquidation with the aim of minimizing a combination of volatility risk and transaction costs arising from permanent and temporary market impact. For a simple linear cost model, we explicitly construct the efficient frontier in the space of time-dependent...

We present a highly-intuitive closed-form delta-hedging result for a large investor whose trades generate adverse market impact. Unlike the complete-market or proportional-transaction-cost cases, the agent no longer finds it tenable to be perfectly hedged or even within a fixed distance of being...