portfolio design and optimization within the framework of the markov chain

Return and risk are significant parameters in selecting an optimal portfolio, depending on the portfolio return distribution. in a stochastic process, the markov property causes the future distribution of a random process to be measurable according to the state-transition matrix and the initial process state. according to the main idea of the present study in the optimal portfolio selection, portfolio weights are chosen in a way that the markov property is established for the portfolio return series and the distribution of future portfolio returns is close to the distribution of investor’s expected returns; hence, k-l divergence (kullback–leibler divergence) is utilized as a criterion of closeness. using this idea, an optimal portfolio selection model was designed and implemented in the present study. this optimal portfolio was optimized using a markov approach and according to historical data of 10 indices on the tehran stock exchange from 2009 to 2022 in a six-member state. the optimal portfolio performance evaluation using the sharpe ratio and value at risk criteria indicated that the research model had a higher performance than the mean-variance and weight parity models.