ABSTRACT Title: Multi-period Risk Measures and Multi-stage Portfolio Selection Prob lems Descipline: Mathematics Applicant: Jia Liu Supervisor: Prof. Zhiping Chen ABSTRACT The essence of financial decision making problems is to pursuit higher profits, which is accomplished through choosing the optimal investment policy. Therefore, the optimal portfolio selection problem is always an important topic in financial optimization and operations research. Single-period portfolio selection problems have been extensively investigated, while the multi-period portfolio selection problem is attracting more and more attention in fields such as financial engineering and operations research. Espe. cially in China, the short-term investment can not earn stable profits any more due to the market depression. Hence, finding robust and optimal multi-stage portfolio becomes an urgent issue. Meanwhile, with the development of economic globalization, the market environment becomes more complicated, and the market state changes rapidly, it is thus very difficult for investors to obtain the complete market information. All these facts re- quire us to construct new multi-period risk measures which can capture the dynamics of market environment, and to construct resulting multi-stage portfolio selection models to gain stable returns while avoiding extreme risks. By simultaneously utilizing statistical methods and some modern optimization techniques, we will systematically investigate these issues from the following perspectives (1)As the basis for constructing new multi-period risk measures under complex market environment, we first review fundamental properties of multi-period risk measures, es pecially its time consistency. According to their structural properties, we divide current multi-period risk measures into three classes: terminal wealth risk measures, additive risk measures and recursive risk measures. Then we derive their generic forms. For each class, we survey typical formulations of multi-period risk measures in the literature, dis- cuss their mathematical properties and relationships (2)In order to describe the time-varying property of stochastic market, we propose a joint information framework by combining the regime switching model, the factor model The work is supported by the National Natural Science Foundation of China(Grant numbers: 70971109 71371152,11571270)ABSTRACT Title: Multi-period Risk Measures and Multi-stage Portfolio Selection Prob￾lems Descipline: Mathematics Applicant: Jia Liu Supervisor: Prof. Zhiping Chen ABSTRACT The essence of financial decision making problems is to pursuit higher profits, which is accomplished through choosing the optimal investment policy. Therefore, the optimal portfolio selection problem is always an important topic in financial optimization and operations research. Single-period portfolio selection problems have been extensively investigated, while the multi-period portfolio selection problem is attracting more and more attention in fields such as financial engineering and operations research. Espe￾cially in China, the short-term investment can not earn stable profits any more due to the market depression. Hence, finding robust and optimal multi-stage portfolio becomes an urgent issue. Meanwhile, with the development of economic globalization, the market environment becomes more complicated, and the market state changes rapidly, it is thus very difficult for investors to obtain the complete market information. All these facts re￾quire us to construct new multi-period risk measures which can capture the dynamics of market environment, and to construct resulting multi-stage portfolio selection models to gain stable returns while avoiding extreme risks. By simultaneously utilizing statistical methods and some modern optimization techniques, we will systematically investigate these issues from the following perspectives* . (1) As the basis for constructing new multi-period risk measures under complex market environment, we first review fundamental properties of multi-period risk measures, es￾pecially its time consistency. According to their structural properties, we divide current multi-period risk measures into three classes: terminal wealth risk measures, additive risk measures and recursive risk measures. Then we derive their generic forms. For each class, we survey typical formulations of multi-period risk measures in the literature, dis￾cuss their mathematical properties and relationships. (2) In order to describe the time-varying property of stochastic market, we propose a joint information framework by combining the regime switching model, the factor model *The work is supported by the National Natural Science Foundation of China (Grant numbers: 70971109, 71371152, 11571270). III