The Research Of Some Portfolio Model Based On Robust Optimization

Portfolio by typically refers to individuals or institutions have stocks, bonds and derivatives, and other securities of a collection of investment. Traditionally portfolio model is a classic example of mathematical programming in the input parameters accurately known and equal to the nominal value under the assumption of model, and use of the existing mathematical programming method to solve the model, the optimal solution. However, these methods do not consider the uncertainty of modeling data quality and feasibility, the effect of in this paper, the robust optimization method was used to construct a portfolio model to solve the portfolio model is easily affected by the input parameters of the problem.In this paper, on the one hand trying to robust optimization methods in different portfolios model to establish a framework of a system, on the other hand make up only part of the country at present robust portfolio optimization model to study, while ignoring transaction costs and practical constraints the impact of robust portfolio optimization model, enrich the robust portfolio optimization model range of applications, while for its derivatives (including transaction costs and practical constraints) the robust optimization model the following conclusions:(1) Compared to robust portfolio optimization model with the traditional model portfolios (corresponding models are compared, namely as:Robust Mean-CVaR portfolio (RCVaR) model compared to the mean-Conditional Value at Risk (CVaR) Portfolio (MCVaR) model) is more stable returns, higher investment performance.(2) Introduction of transaction costs. The transaction costs for introducing robust portfolio optimization model to analyze the optimized model, such a portfolio optimization model is solvable, efficient, robust, and its investment portfolio returns, portfolio risk and portfolio performance performance are better than the transaction costs directly introduced into the portfolio optimization model, the introduction of transaction costs show robust optimization model is still valid. Based on transaction costs at the same time robust optimization model introduced practical constraints, it will further enhance portfolio returns, portfolio risk and performance aspects of portfolio performance.(3) Introduction of real constraints. After excluding transaction costs for robust optimization model into real constraints drawn:first, the degree of decentralization impact on the portfolio. Prior to the portfolio weights of each asset fully dispersed, with an increase in the degree of dispersion portfolio, portfolio income reduced portfolio risk is reduced, which is the same as the actual situation in the capital markets; weight fully dispersed the assets in the portfolio right after, With the increase in the degree of dispersion of the portfolio, the portfolio income equally reduced, but increased the risk of the portfolio. Second, the level of liquidity portfolio affected. When the portfolio managers of the minimum liquidity requirements for the higher level of the portfolio, the greater the risk of the portfolio, increasing the income portfolio, the portfolio performance decreases, and vice versa, which is the reality of stock market investment decisions exactly the same. Third, the upper and lower bounds constraints affecting asset portfolio. Income from the portfolio and performance point of view, by adjusting the assets in the portfolio constraint bounds can be achieved with the portfolio managers adjust the desired minimum income portfolio, portfolio diversification and liquidity levels the same degree of effectiveness.The main contents of this paper are:Chapter 1 is an introduction. Introduces the background and significance of the research, innovation and shortcomings.Chapter 2 is a modern portfolio optimization theory Summary development. Markowitz introduced since 1952 classic "Assets Select" On the first of its kind since the financial and mathematical analysis, portfolio optimization model and the challenges facing the development of the theory and practical applications, including transaction costs, constraints and other constraints of reality earnings and sensitivity and robustness optimization methods such as variance; in addition, the portfolio optimization model and related fields are also faced with new trends are reviewed, such as decentralized methods, risk parity model, mixing different combinations of expected return and more optimization problems, making the portfolio optimization model development process have an overall profile.Chapter 3 is a logarithmic robust portfolio optimization models. Based on asset prices lognormal distribution based on the assumption introduced worst case scenario (ie, value at risk), consider the relevance of each asset raised three asset relationship between the logarithm of the robust portfolio optimization model:the worst scenario independent Number of robust asset portfolio optimization (WCIALRO) model, the special assets associated with the worst scenario for the number of robust optimization (WCCASCLRO) typically associated with assets under worst case scenario for the number of models and robust optimization (WCCAGCLRO) model; and gives general association assets (WCIALRO) model that ACWCIALRO model and has an upper bound constraint worst scenario independent asset logarithm robust portfolio optimization under the constraint of having the upper bound on the number of worst case scenario robust optimization (WCCAGCLRO) model that ACWCCAGCLRO model; the introduction of transaction costs under the worst case scenario based on the number of independent asset robust portfolio optimization model was constructed including transaction costs under the worst case scenario for the number of robust optimization independent asset portfolio (TCWCIALRO) model.Chapter 4 is the robust CVaR portfolio optimization models. Analysis of uncertainty set symmetric and asymmetric uncertainties robust set CVaR model portfolio optimization strategy, build the model expected returns are uncertain set of rectangular symmetry: Robust Mean-CVaR portfolio (RCVaR) model and derived model Robust Mean-CVaR portfolio including transaction costs (RTCCVaR) model and the robust mean-CVaR portfolio based on real constraint (RCRCVaR) model, the expected return are asymmetrical set model:asymmetric uncertainty robust risk conditions set-the value of the portfolio (RACVaR) model and its derivatives transaction cost model based on asymmetric uncertainty robust set of conditional value at risk portfolio (RTCACVaR) model based on the reality of the constraints under asymmetric uncertainty robust set of conditions and risks-Value Portfolio (RCRACVaR) model.Chapter 5 is the robust optimization mean-semi-absolute deviation model. In the mean-semi-absolute deviation model (MSAD), based on the average cost to build a transaction including transaction costs-semi-absolute deviation portfolio (TCMSAD) model; at the same time based on transaction costs mean-semi absolute deviation portfolio (TCMSAD) model using Lu Stick to build robust optimization method transaction costs mean-semi-absolute deviation portfolio model (RTCMSAD) and robust transaction costs mean real constraint-based-semi-absolute deviation portfolio model (RCRTCMSAD), enrich the application model and RMASD model MSAD.Chapter 6 is the robust optimization mean-absolute deviation model. Robust mean-absolute deviation (RMAD) model based on the actual situation of Chinese securities market, proposed a simplified model for RMAD our investment portfolio management. At the same time, the use of the same data, the optimal solution RMAD model portfolio with the results of other scholars to conduct performance analysis model proved RMAD simplified model is superior to compare models selected from earnings, risk and investment performance perspective.Chapter 7 is the robust multi-objective optimization goal programming model portfolio. Based on multi-objective goal programming portfolio (MGM) model, using robust single objective goal programming (RSGM) modeling method is proposed robust multi-objective goal programming portfolio (RMGM) model extends the robust optimization methods Goal programming model portfolio of applications.Chapter 8 is the robust optimization model portfolio tracking error. Robust optimization investment portfolio tracking error (RTE) model portfolio optimization based on the tracking error (TE) containing tracking error Robust Optimization investment portfolio transaction costs (TCRTE) model and a numerical example is also given by Numerical examples are found after the introduction of transaction costs will affect investment decisions, and even get the opposite conclusion, which for the portfolio practice is helpful.Chapter 9 is the conclusion and prospect of research.