OPTIMAL CONSTRAINED PORTFOLIO ANALYSIS FOR INCOMPLETE INFORMATION AND TRANSACTION COSTS

Asset price dynamics can be explained by means of a mathematical model. The problem is that these models simulate real situations, which are not always attainable. The fact that real markets are characterized by inadequate information is one of the challenging issues that mathematical models must solve as they are compelled to make assumptions about the financial market. This paper aims to introduce and create a unique Markov model for incomplete information in order to address these deficiencies and solve the portfolio optimization problem while taking pricing and risk minimization management into account. We assume that trading in securities occurs in discrete time increments. Investors can trade in securities and track their short-term pricing. We make the following assumptions: Short-selling is not permitted on the market, all assets have equal selling and buying prices, trading costs apply, and investors can buy and sell an infinite number of shares on an arbitrage-free market. We suggest the construction of an observer for partial information to address the portfolio optimization problem. The ideal portfolio and the problem observer are the results of the process. We provide the formulae for recovering the important variables. We can recover the observation kernel from the resulting observer, which is understood to be the manager's intuition during the decision-making process. This is the main result of this paper. To the best of our knowledge, this is the first time that a solution of this kind for portfolio optimization using partial data has been proposed in the literature. Under these assumptions, a Markov model is used in a numerical example that demonstrates the effectiveness and use of the suggested approach for creating workable portfolio models.