Optimal Portfolio Model And Arithmetic Analysis Under The Constraints Of Risk

H.Markowiz put forward to mean-variance model for portfolio selection at the earliest stage in 1952. This theory was through the development of more than 40 years, having become the theoretical core in modern portfolios, having become hot research problem in financial mathematical theories and financial engineering techniques. In Markwitz's portfolio theory, it is assumed that all the investors disgust the risk, and asset returns are random variables, then we utilize the expectation value (mean) of return (rate) to measure the investment return, and the variance of return (rate) to measure the investment risk. Decision method is giving the expected return, minimize the risk; or giving the risk, maximize the expected return. Different from Markwitz's risk methodology, VaR presented in recent years is a new approach to estimate market risks. In the normal market conditions, a VaR measure is the highest possible loss over a certain period of time at a given confidence level.In this article, we propose synthesizing the traditional theory with the theory of risk management with VaR together. We have done below a few aspect researches:1.Present a portfolio model under constraints of both VaR and free-risk investment or free-risk loan. This model reflected that expected return (rate) of portfolio attain some a value, meanwhile we request the highest possible loss (should) be ensured not to exceed VaR.2. Study valid portfolio and efficient frontier calculation in different risk restriction. And under the assumption that portfolio returns are normally distributed, we evaluate the efficient portfolios, and calculate the formula of efficient frontier of portfolios.3. Based on the normal assumption for the distribution of financial returns, we characterize the mean-CVaR efficient set, and present efficient investment proportion of minimum CVaR portfolio.