Dynamic optimal asset allocation in a multivariate setting

Abstract

This article analyzes a portfolio allocation problem to determine how resources should be allocated among several possible investments. Investors aim to maximize the profit of an investment while also considering the risks arising from infrequent events. The global financial crisis, which began with subprime mortgages in the United States, has fundamentally changed the way we invest. As we know, investors want to maximize returns while controlling the risk associated with a particular investment. This behavior must be modeled mathematically using optimal control theory and expected utility maximization. A continuous-time market is considered in a multivariate context in which there exist risky asset classes and a risk-free asset with a constant interest rate. We deviate from the traditional approach by considering co-precision, the inverse of the covariance matrix, as a measure of risk. The optimal weights obtained are proportional (inversely) to the risk measure (volatility). The model is tested on 11 asset classes used by a large company also carrying out a stress test on the jump component to analyze the allocation of the investors’ portfolio in a real context.