Al Ramz Quantitative Research focuses on mathematical methods to deal with financial markets for equities, fixed income and their derivatives. Current activity focuses on traditional sciences, like probability theory, the use of integral operators and Boltzmann equations, applications of complex-variable functions to time-series, and the theory of generalized functions. It also engages, by time to time, in blended approaches with machine learning and AI.
We present a systematic approach to maximize the Sharpe ratio of a portfolio composed of several assets and/or strategies. This is also a common problem in multi-strategy hedge funds. We begin with the case of two assets, or strategies, and derive an exact analytical solution. Then, we draw a path to the more complex case of several assets or strategies, and we outline the approach based on numerical methods, along with the connection to quadratic forms. Some mathematical preliminaries are also presented in order ensure the reader is familiar with some theory of generalized functions, their integrals, and their applications to probability.