Investment opportunities and VaR constraints mean - variance model portfolio
|Keywords||Chance constrained VaR constraint Portfolio selection Risk - free securities Optimal solution|
Portfolio theory to study how limited kinds of assets to invest in reasonable balance makes the expected return and risk in the case of future results uncertain. Harry Markowitz first proposed in 1952 a scientific portfolio selection method - mean - variance method, has laid a solid foundation for modern portfolio theory, since then, the expected rate of return to measure securities portfolio returns, variance or variance measure of Securities portfolio risk analysis framework in the financial sector has been established. Investment opportunities constraints and constraint of VaR is based on the expected rate of return and a given confidence level determined oriented. Securities yield a normal distribution under the premise under a class of short sales and investment opportunities and VaR constraints mean - variance model, the standard mean - variance analysis of Efficient Portfolio Set made further refinement. The main innovation of this paper are: (1) the risk-free asset to introduce investment opportunities under the constraint of mean - variance model, (2) dual constraints of the investment opportunities and VaR portfolio, the establishment of a mathematical model; above two types of models, the existence and uniqueness of the optimal solution, and gives an analytical expression of the optimal solution. The full text is divided into four chapters. The first chapter introduces the standard mean - variance model and the mean - variance efficient set \The second chapter focuses on the presence of risk-free asset investment opportunities under the constraint of mean - variance model, which include risk-free asset will only be allowed to lending not allowed to borrow and borrowing and lending interest rates ranging from two cases. Derived both cases mean - variance efficient frontier expression that portfolio selection in investment opportunities constraints mean - variance model existence of optimal solutions and uniqueness, the analytical expression of the optimal portfolio . Chapter VaR constraint on the portfolio selection under the constraints of the investment opportunities in the mean - variance model portfolio selection model to construct the dual constraints, are discussed according to the risk-free asset exists or not. Risk-free asset existence, they will only be allowed by the risk-free asset lending are not allowed to borrow and borrowing and lending interest rates ranging discussion is divided into two cases, the same optimal solution Existence and Uniqueness of the most the analytical expression of the optimal solution. Chapter wealth of dynamic continuous time mean - variance model that chance constrained and VaR constraints that may be encountered and need to be resolved.