Publication at Faculty of Mathematics and Physics |

2015

A multistage stochastic optimization is a tool which enables to manage portfolio in constantly changing financial markets by periodically re-balancing its structure in order to achieve desired target. This paper presents a decision-making process where the objective function is to maximize investor's expected utility over a finite time horizon, namely we consider a class of non- separable multivariate utility functions.

Features of utility functions already contain the information on investor's risk attitude thus basically no risk con- straints are necessary. However, the solution cannot guarantee that the investor does not find herself in an undesirably risky position within the investment horizon.

We therefore suggest a reformulation of the underlying problem by adding an extra constraint on an upper bound of risk premiums. The performance of the suggested model is demonstrated by optimizing the allocation of wealth at each time instance to two different assets one of which is assumed to be risk-free.

The stochastic character of the problem is provided in the form of a scenario tree. Experiments are conducted to compare performance of the underlying formulation (considering no explicit constraints on the risk exposure) with the extended one (considering constraints on the risk exposure).