Artificial Intelligence in Finance, Volume 2: Reinforcement Learning Theory and Practice
First published:
ISBN: 9781782724544
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Portfolio optimisation
Miquel Noguer i Alonso, Daniel Bloch and David Pacheco Aznar
Portfolio optimisation
Preface
Introduction
Markov decision problems
Learning the optimal policy
Reinforcement learning revisited
Temporal difference learning revisited
Stochastic approximation in Markov decision processes
Large language models: reasoning and reinforcement learning
Deep reinforcement learning
Applications of artificial intelligence in finance
Pricing options with temporal difference backpropagation
Pricing American options
Daily price limits
Portfolio optimisation
Appendix
13.1 INTRODUCTION
Portfolio optimisation is about computing the optimal weights in a portfolio of assets for a given investment horizon by maximising some objective function. The modern portfolio theory (MPT) (Markowitz 1952a, 1959) entails a two-step construction process.
Estimate population moments. Compute the first two moments of asset returns over a given horizon; this is a prediction problem for the vector of expected returns and covariance matrix.
Portfolio construction. Optimise a mean–variance criteria over possible combinations of assets; this is a quadratic optimisation problem.
Researchers and practitioners have devised several techniques for estimating expected returns and the covariance matrix (James and Stein 1961; Black and Litterman 1992). However, it is extremely difficult to estimate returns accurately because of the lack of a long time series of data (Merton 1980). Further, estimates of variance-covariance are seldom well behaved. This difficulty in estimating the first two moments of returns leads to the error-maximising problem (EMP) of the mean–variance portfolio (Best and Grauer 1991). That is, we get unstable and extremely positive and negative weights in step
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