The financial risk not only affects the normal operation and the survival of the industrial and commercial enterprise and the financial organization, but also threats to the stable development of a country and even the global finance economy. For recent years, the serious results caused by the frequently occurring financial crisis fully show this point.Therefore, the financial risk guardance becomes one of the core works that the industrial and commercial enterprise and the financial organization carry on management and operation. The scientific and reasonable profolio optimization decision-making has the vital practical significance to efficiently control the finance risk and to optimize resources allocation.In the thesis, considering the fact situation that the transaction number is an integer and associated with portfolio construction is a fee for purchasing assets in the stock market in China at present, increasing minimal transaction unit constraint, and unifying the actual transaction cost situation, we propose the below profolio optimization models.(1) With the concave transaction cost function more conforming to the actual situation, we introduce condition risk value (CVaR) to measure profolio risk, and propose mean- CVaR concave integer programming model under concave transaction costs and minimal transaction unit constraints. In the same time, we give a genetic algorithm to solve this model, and the numerical experiment shows that the model is reasonable and the algorithm is efficient.(2) Under the concave transaction costs function, using the variance of profolio return rate to express profolio risk, and taking the risk-return combination difference as the objective function, we propose Mean-variance D.C- integer optimization model under concave transaction costs and minimal transaction unit constraints. And we structure a genetic algorithm to solve this model, the actual example indicates that the model is reasonable and the algorithm is extremely effective.(3) According to the fact situation that short sale is not allowed, we increase the lower and upper bound constraint of portfolio return. And regarding the probability of expect return and the probabilityof loss risk as the objective functions, we propose the multi-objective integer programming model with probability criterion based on minimal transaction unit. Moreover, under the condition that the return rate of portfolio has normal distribution, we transform this probabilistic model equally into the definite optimization model.With the linear weight method, we transform the multi-objective programming into the simple programming, and use the genetic algorithm to solve this model. The actual example shows that the model is reasonable and the algorithm is very effective.(4) With the non-convex and non-concave typical transaction costs function more conforming to the actual situation, we propose portfolio optimization model with safety -first criteria based on CVaR under typical transaction costs. Moreover, under the condition that the return rate of portfolio has normal distribution, we transform this probabilistic model with safety -first criteria equally into the definite optimization model. By the optimizing method, we propose a method and relevant results of determining the optimal portfolio, its corresponding expectation of return and its value of conditional value-at-risk satisfying the given safety criteria on the portfolio expectation return-conditional value-at-risk efficient frontier according to the three types of safety-first criteria. |