| Portfolio selection optimization model is often used to provide investors with investment decisions and risk evaluation.However,in practical problems,investment return rate is affected by many factors such as economic environment,natural events and so on,so we cannot know its specific distribution.How to invest when the return rate distribution is uncertain is one of the hot issues in the field of optimization in recent research.The main research of this thesis is to study the portfolio optimization problem with unknown distribution by using distributionally robust optimization theory.First,we study the chance constraint stochastic optimization problem with unknown distribution,where?is a random variable and its distribution p is unknown.Empirical random variable?0 and empirical distribution p0 are obtained by using historical data.According to empirical distribution and Wasserstein metric,we construct the uncertain setof unknown distribution.Then we transform this uncertain optimization problem into a deterministic optimization problem by measure transformation and entropy regularization.We apply the above conclusions to the uncertain portfolio selection problem and convert the Va R model and the CVa R model to deterministic problem respectively.Finally,we use sample average approximation to solve the equivalent problems,and prove the convergence of the sample mean function.The first part in this thesis introduces the background of the main problems studied in this paper.The second part introduces the basic concepts of this paper.The third part establishes stochastic optimization problem with chance constraint.We transform the original problem into an optimization problem with definite distribution by using measure transformation and duality theory.The fourth part applies the above methods to Va R model and CVa R model.The last part provides the sample average approximation method for solving the transformed Va R model and CVa R model. |
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