Stochastic partial differential equations and portfolio choice

A new approach to portfolio management will be introduced. Complementing the traditional one, which is based on terminal time criteria, this approach yields investment processes across all times and offers flexibility to address important questions in portfolio management like, among others, investment choice for different benchmarks, market views and time horizons. The investment performance process solves a stochastic partial differential equation. One of the novel elements in this new approach is the performance volatility process. The class of admissible volatilities will be discussed. Results on the solutions of the performance SPDE and the form of optimal investment policies will be presented.