In recent years, the interest of investors has shifted to computer(cid:173) ized asset allocation (portfolio management) to exploit the growing dynamics of the capital markets. In this paper, asset allocation is formalized as a Markovian Decision Problem which can be opti(cid:173) mized by applying dynamic programming or reinforcement learning based algorithms. Using an artificial exchange rate, the asset allo(cid:173) cation strategy optimized with reinforcement learning (Q-Learning) is shown to be equivalent to a policy computed by dynamic pro(cid:173) gramming. The approach is then tested on the task to invest liquid capital in the German stock market. Here, neural networks are used as value function approximators. The resulting asset alloca(cid:173) tion strategy is superior to a heuristic benchmark policy. This is a further example which demonstrates the applicability of neural network based reinforcement learning to a problem setting with a high dimensional state space.