A generalized measure for the optimal portfolio selection problem and its explicit solution

In this paper, we offer a novel class of utility functions applied to optimal portfolio selection. This class incorporates as special cases important measures such as the mean-variance, Sharpe ratio, mean-standard deviation and others. We provide an explicit solution to the problem of optimal portfolio selection based on this class. Furthermore, we show that each measure in this class generally reduces to the efficient frontier that coincides or belongs to the classical mean-variance efficient frontier. In addition, a condition is provided for the existence of the a one-to-one correspondence between the parameter of this class of utility functions and the trade-off parameter λ in the mean-variance utility function. This correspondence essentially provides insight into the choice of this parameter. We illustrate our results by taking a portfolio of stocks from National Association of Securities Dealers Automated Quotation (NASDAQ).