Stochastic portfolio optimization by diversity-weighted portfolio approach

‎‎The portfolio optimization problem, including portfolio selection, typically aims to maximize return and minimize risk. In this paper, we discuss about increasing use of stochastic portfolios in investments and aim to create optimal portfolios. It follows the relative wealth process of these portfolios, outperforms the market portfolio over sufficiently long time-horizons. In this regard, initially, a model of the market is presented by the stochastic portfolio theory (SPT) and features like Growth rate, Excess growth rate are mentioned. Then, functionally-generated portfolios are defined by using diversity weighted portfolios with parameters p ∈ (0, 1), p < 0 and combination of them. Finally, by obtaining the daily closing price of 10 stocks in Tehran Stock Exchange (TSE) ,the performance of diversity weighted portfolios is investigated.