Portfolio Selection Based On Uncertain Cross-entropy

Uncertainty theory is a branch of axiomatic mathematics to deal with human’s belief degree. As the core concept in uncertainty theory, uncertain variable is a real valued function on an uncertainty space. Cross-entropy is a concept which measures the difference between two uncertain variables. This thesis proposes a new kind of cross-entropy called sine cross-entropy, which is used to solve the portfolio selection problem.Portfolio selection aims at a more profitable return and less risk by allocate one’s capital to a large number of securities. This thesis proposes new portfolio selection models by minimizing the sine cross-entropy between the investment return and the prior return. Meanwhile, the thesis adds conditions which restrict on the return as expected value and risk as variance to construct the first model. In addition, the thesis presents another model by controlling the chance of bad outcome.To solve these models, we transform these uncertain programming problems to the crisp ones by uncertainty theory. At last, there are some numerical experiments to test these models.The contributions of this thesis are:? It proposes a definition of uncertain sine cross-entropy, and proves some proper-ties;? It builds two models of portfolio selection problems based on uncertain sinecross-entropy;? It presents the genetic algorithm of the problem and does numerical experiments.