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.

This paper enhances the Q-Iearning algorithm for optimal asset alloca(cid:173) tion proposed in (Neuneier, 1996 [6]). After testing the new algorithm on real data, the possibility of risk management within the framework of Markov decision problems is analyzed. The proposed methods allows the construction of a multi-period portfolio management system which takes into account transaction costs, the risk preferences of the investor, and several constraints on the allocation.

This paper enhances the Q-Iearning algorithm for optimal asset allocation proposed in (Neuneier, 1996 [6]). The new formulation simplifies the approach by using only one value-function for many assets and allows model-free policy-iteration. After testing the new algorithm on real data, the possibility of risk management within the framework of Markov decision problems is analyzed. The proposed methods allows the construction of a multi-period portfolio management system which takes into account transaction costs, the risk preferences of the investor, and several constraints on the allocation. 1 Introduction

This paper enhances the Q-Iearning algorithm for optimal asset allocation proposed in (Neuneier, 1996 [6]). The new formulation simplifies the approach by using only one value-function for many assets and allows model-free policy-iteration. After testing the new algorithm on real data, the possibility of risk management within the framework of Markov decision problems is analyzed. The proposed methods allows the construction of a multi-period portfolio management system which takes into account transaction costs, the risk preferences of the investor, and several constraints on the allocation. 1 Introduction

This paper enhances the Q-Iearning algorithm for optimal asset allocation proposedin (Neuneier, 1996 [6]). The new formulation simplifies the approach by using only one value-function for many assets and allows model-freepolicy-iteration. After testing the new algorithm on real data, the possibility of risk management within the framework of Markov decision problems is analyzed. The proposed methods allows the construction of a multi-period portfolio management system which takes into account transaction costs, the risk preferences of the investor, and several constraints on the allocation. 1 Introduction

In recent years, the interest of investors has shifted to computerized 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 optimized by applying dynamic programming or reinforcement learning based algorithms. Using an artificial exchange rate, the asset allocation strategy optimized with reinforcement learning (Q-Learning) is shown to be equivalent to a policy computed by dynamic programming. 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 allocation 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.

In recent years, the interest of investors has shifted to computerized 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 optimized by applying dynamic programming or reinforcement learning based algorithms. Using an artificial exchange rate, the asset allocation strategy optimized with reinforcement learning (Q-Learning) is shown to be equivalent to a policy computed by dynamic programming. 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 allocation 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.

Ralph Neuneier* Siemens AG, Corporate Research and Development Otto-Hahn-Ring 6, D-81730 Munchen, Germany Abstract In recent years, the interest of investors has shifted to computerized assetallocation (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 optimized byapplying dynamic programming or reinforcement learning based algorithms. Using an artificial exchange rate, the asset allocation strategyoptimized with reinforcement learning (Q-Learning) is shown to be equivalent to a policy computed by dynamic programming. Theapproach is then tested on the task to invest liquid capital in the German stock market. Here, neural networks are used as value function approximators.