Dynamic Entropy Portfolio Selection Models Under Transaction Costs

With more complex in modern financial markets, investors have to face more un-certainty phenomenon while making investment decisions. In this paper, due to the in-fluences of random uncertainties and fuzzy uncertainties on investment risks, we raise three entropy models of different states of different periods to suit different needs of investors of different markets.The first chapter describes the importance of the portfolio selection problems un-der uncertain environments primarily and recalls existing models like mean-variance models, stochastic portfolio models, fuzzy portfolio models, fuzzy stochastic portfolio models, random fuzzy portfolio models and entropy portfolio models. And definitions of fuzzy numbers, interval numbers, algorithm of fuzzy random variables, as well as the definition of several entropies used in the dissertation are given in the last of this chapter.The core concept of this paper is uncertainty. Because of the stringent implied con-ditions of traditional mean-variance model, incremental entropy and hybrid entropy are used to replace mean and variance in the second chapter. To meet the actual situation, fuzzy random variables are applied as the expected returns and the historical data are estimated as the left and right width of fuzzy numbers. In order to facilitate investors to adjust the proportion of investment, state changes become the sole criterion to adjust assets. As long as the income values of model exceed investors’predetermined values, system will automatically adjust the ratio of investment. Finally, because of the exis-tences of constraints, genetic compromise algorithm is added to get the exact solution of the two-goal planning model to attain the compromise investment strategy. Through 8 stocks of the SEE 300, results of incremental-hybrid entropy model are better than traditional mean-variance model and MCMC method.The third chapter firstly discusses types of risks. In real investment market, be-side the systemic risk mentioned portrayed by hybrid entropy mentioned in chapter 2, there is also subsystem risks caused by asymmetric information and other internal accidents. Through maximizing Shannon entropy, proportion investments become op-timum choices contributing to minimize subsystem risks. However, it is very difficult to meet the conditions of proportion investment as it may decrease the return values. Thus, Yager entropy is used to measure the subsystem risk. The advantages of market circumstances of incremental-hybrid-Yager’s entropy model are discussed at the end of this chapter.With existence of incompleteness and missing data in statistic, it is often difficult to obtain the accurate values of left width and right width of fuzzy numbers by Markov chain. In chapter 4, interval fuzzy numbers are presented as a special fuzzy numbers to describe multi-state portfolio choices. Changing the triangle fuzzy numbers to interval numbers, we get the new model, and particle swarm optimization method is added to obtain solutions.