Multi-period risks in portfolio selection

This interdisciplinary project develops the mathematical foundations and numerical techniques of optimal dynamic portfolio selection under multi-period risk constraints. We look at the following portfolio selection problem in continuous and discrete time. Under proportional transaction costs an investor allocates funds to multiple assets and a bank account, so as to maximise the long-term expected growth rate, utility of terminal wealth, or utility of consumption - all under dynamical risk constraints on the wealth process. This describes the situation of financial institutions which have some economic capital at their disposal and try to conduct business so as to maximise profits and stay within the limits given by economic capital. The results envisaged can also be applied to market risk measurement on long time horizons, which is relevant for fully integrated market and credit risk measurement. We proceed in six steps: (1) investigate properties of multi-period risk measures and justify the choice of appropriate risk measures, (2) continuous and discrete time modeling of portfolio selection with multi-period risk measures, (3) investigate and compare solution structures in continuous and discrete time, (4) develop evolutionary algorithms for discrete and discretised optimisation problems, (5) develop LP- and bundle methods for the solution of discrete optimisation methods, (6) compare performance, accuracy and robustness of the different solution methods.