| Portfolio theory,as an important element of finance research,has laid the foundation for modern portfolio theory since Markowitz first proposed the Mean-Variance model in 1952.However,in recent years,the frequent outbreak of financial crises represented by the U.S.Subprime Mortgage Crisis and European debt crisis has brought a huge impact to the world economy.As the financial market is an extremely complex non-linear system,especially the frequent financial crises in recent years have led to structure break of the financial market,causing violent shocks in the financial market and making the financial portfolio face more difficulties and challenges.Especially in the current environment of international financial market integration,investors need to as much as possible hedge market risks,proactively optimize asset allocation,reduce the risk crisis in investment practice,and obtain higher investment returns.Therefore,in the context of structure break in financial markets,how to effectively prevent financial crises and construct effective portfolio optimization models has become one of the main issues that need to be addressed in current financial research.As we all know,with the rapid development of market economy and the trend of global economic integration,financial capital can be rationally allocated in the world,but at the same time,it also increases the possibility of financial crisis.When a certain financial market or financial asset has structure break,it may trigger a significant volatility trend in the related financial markets or financial assets,i.e.,risk contagion between financial markets or financial assets.Research shows that structure break is a prerequisite for risk contagion in financial markets,but according to Makowitz's portfolio theory,when there is risk contagion among the constructed portfolio investment assets,it may lead to difficulties in achieving diversification of the portfolio,thus making the portfolio suffer from large economic losses.Therefore,how to construct a portfolio optimization model when there may be risk contagion relationship in financial markets or financial assets has become a key issue of current research.Traditional portfolio theory is mainly based on a single perspective of return maximization or risk minimization,and most portfolio models are static models,while the return of financial assets often presents a non-linear,dynamic and complex structure,and portfolio models constructed only based on return maximization or risk minimization may behave in the actual investment behavior as The phenomenon of "over-investment blindness" or "under-investment caution" may lead to failure or additional losses in portfolio investment practices.Therefore,in the context of structurel break and risk contagion in financial markets,it is important to examine how to find an optimal point in "maximizing return and minimizing risk" from two perspectives,and to conduct dynamic time-varying portfolio optimization research based on this,so as to enrich the theory of portfolio optimization and provide new research ideas for financial portfolio optimization.This thesis aims to provide a new research idea for financial portfolio optimization research.In this thesis,we use mathematical statistics and computer technology to construct a time-varying portfolio optimization study of high-dimensional financial markets(including stock market,exchange rate market and energy market),taking the possible structure break and risk contagion relationship of financial markets as the research constraints.Firstly,the HMM and ICSS models are introduced to identify the structure breaks in the financial market;Secondly,the dynamic R-Vine Copula model is constructed to study the risk contagion relationship among financial markets based on the results of the structure breaks in the financial market to ensure the accuracy of the portfolio optimization research;Thirdly,the Mean-CVa R model is used to study the risk contagion relationship among financial markets from the actual financial practice.Finally,based on the Mean-CVa R model,we construct a high-dimensional time-varying portfolio optimization model that satisfies both return maximization and risk minimization,so as to propose countermeasures for financial investment institutions to make macro-financial management decisions and risk regulators to respond to and prevent investment risks,in order to maintain economic security and promote economic prosperity.The research of this thesis has important academic value and practical significance.The specific research contents are as follows.(1)Research on portfolio optimization under the volatility structure break.In this paper,the traditional MRS model is firstly used to portray the financial volatility structure break,and the HMM-ICSS model is constructed to portray the volatility structure break due to the strong subjectivity of the traditional MRS model in the volatility structure break portrayal,which may lead to the failure of the volatility structure break portrayal.Second,based on the results of the volatility structure break study,we construct a portfolio optimization model to compare the portfolio optimization effects of static portfolio optimization and time-varying portfolio optimization models with and without volatility structure break.The empirical study proves that the HMM-ICSS model can more effectively portray the structure break in financial volatility,and the Mean-CVa R time-varying portfolio optimization model has significant accuracy and reliability under the volatility structure break.(2)Portfolio optimization research under financial risk contagion.First,this paper uses the traditional risk contagion measurement model based on the multivariate Copula model to study the risk contagion relationship among financial assets,because the traditional risk contagion model tends to fall into the circle of "curse of dimensionality",which cannot accurately portray the risk contagion relationship among high-dimensional financial markets.Second,based on the results of the risk contagion relationship,we construct a portfolio optimization model to compare and analyze the portfolio optimization effect of static portfolio optimization model and time-varying portfolio optimization model with and without the risk contagion constraint;finally,we test the risk contagion relationship of financial assets and the Finally,the risk contagion relationship of financial assets and the portfolio optimization model are tested to ensure the reliability and accuracy of the portfolio optimization study under risk contagion.The empirical study proves that the R-Vine Copula model constructed in this paper can more effectively portray the risk contagion relationship among high-dimensional financial assets,and the Mean-CVa R-based time-varying portfolio optimization model under risk contagion can not only achieve risk minimization,but also obtain higher investment returns.(3)The study of portfolio optimization under the financial volatility structure break and risk contagion.Since the financial volatility structure break is a prerequisite for the occurrence of financial risk contagion,a study of risk contagion based on the volatility structure break is conducted for financial assets.First,the HMM-ICSS model is used to analyze the volatility structure break;second,the results of the volatility structure break study of financial assets are used to construct the R-Vine Copula model to characterize the possible risk contagion relationship between high-dimensional financial assets;third,based on the results of the volatility structure break and risk contagion study,a high-dimensional time-varying portfolio optimization model is constructed in order to more effectively estimate the time-varying portfolio investment weight coefficients that satisfy both the maximization of investment returns and the relative minimization of financial risks,this paper constructs a new algorithm,the High-dimensional Spatial Rotation Projection algorithm,which can quickly and effectively estimate the model parameters under the dual-objective constraint,enriching and developing the portfolio method,and comparing and analyzing.Finally,the Sharpe ratio is used to test the portfolio optimization model,and the time-varying portfolio optimization prediction models with different time window lengths are also constructed to further test the accuracy and robustness of the time-varying portfolio optimization models under structure break and risk contagion.The accuracy and robustness of the time-varying portfolio optimization model under structural break and risk contagion are further tested.The empirical study proves that the R-Vine Copula model based on volatily structure break can more effectively portray the risk contagion relationship among high-dimensional financial assets,and the time-varying portfolio optimization model based on structure break and risk contagion can obtain higher investment returns while satisfying lower investment risks.The innovation points of this thesis are mainly reflected in the following aspects.(1)In terms of research perspective,we innovate the definition of the volatility structure break and the study of time-varying portfolio optimization.For the definition of financial volatility structure break,most of the existing studies use financial events as the outbreak point for financial structure break,and the research results lack data support,resulting in its reliability is not enough,while this thesis is based on financial data,from two perspectives of financial returns and financial volatility to describe the volatility structure break,which can ensure the accuracy and reliability of the portrayal of financial volatility structure break.For time-varying portfolio optimization research,traditional portfolio optimization is mainly carried out from one of the perspectives of maximizing investment return or minimizing investment risk,but this paper incorporates both maximizing investment return and minimizing investment risk into the same portfolio optimization,and carries out time-varying portfolio optimization from a new research perspective,which further enriches and develops this important research topic of portfolio optimization.(2)In terms of research methodology,it innovates portfolio optimization research theories and methods.Traditional portfolio optimization research is mainly carried out from a single perspective of maximizing investment returns or minimizing investment risks,while for every investor,it becomes the lifelong pursuit of every investor or investment institution to maximize returns and minimize risks at the same time.This paper constructs a multi-objective time-varying portfolio optimization model with the objectives of maximizing return and minimizing risk based on the possible structure break and risk contagion relationship in financial markets or financial assets,and in order to estimate the time-varying investment coefficients in the portfolio investment model more effectively,based on the theoretical ideas of optimization theory,game theory,Euclidean space theory and linear programming.In order to estimate the time-varying investment coefficients in the portfolio optimization model more effectively,a high-dimensional spatial rotation projection algorithm is creatively constructed to estimate the time-varying weight coefficients in the portfolio optimization quickly and accurately.In addition,the algorithm designed in this paper also provides new ideas for solving multi-objective functions,which greatly enriches and develops portfolio optimization theories and models.(3)In terms of research findings,the structure break of financial volatility and financial risk contagion play a more important role in the efficiency of portfolio optimization,but the most influential factor in the study of time-varying state portfolios is the time-varying nature of portfolio optimization models.For portfolio optimization efficiency,it is to some extent the increase in the number of financial markets or financial asset dimensions that enhances it.From the perspective of investment risk minimization,the impact of financial risk contagion on portfolio optimization is significantly stronger than the structure break of financial volatility.In addition,changes in exchange rate market volatility are more likely to induce the occurrence of financial risk contagion effects. |
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