Optimal trading strategies are determined for liquidation of a large single-asset portfolio to minimize a combination of volatility risk and market impact costs. The market impact cost per share is taken to be a power law function of the trading rate, with an arbitrary positive exponent. This...

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...