Modern portfolio theory states that the optimal asset allocation is a function of the mean-variance of the distribution of returns. In practice, these returns are modeled by Gaussian distributions and their parameters are estimated from historical market data, using descriptive techniques of Frequentist statistics. The current dynamics of globalized markets generate random periods of high and low volatility and/or jumps in asset returns, causing regime shifts or structural breaks in the time series of returns, making them non Gaussian. Consequently, modern portfolio theory needs to be adapted to meet these new market conditions. To circumvent the problem of regime shifts, it is proposed to replace the optimization mechanism based on the Sharpe index by the optimization based on the Omega measure. This is because the Omega measure has the advantage of quantifying the risk-return of any probability distribution and not only Gaussian distributions as with the Sharpe index, that is, non Gaussian returns distributions caused by regime shifts are treated naturally by the Omega measure. To circumvent the problem of structural breaks, it is proposed to replace the estimation procedure for the parameters of the distribution of returns, based on Frequentist statistics techniques, by Bayesian statistical techniques. This is because the Bayesian statistic has the advantage of combining public market information (historical return data) with private investor information (prospective market views) allowing to correct the structural break, and subsequently, treating the non Gaussian return using the optimization based on the Omega measure.