西安交通大学：多期风险度量与多阶段投资组合选择问题（博士学位论文）Multi-period Risk Measures and Multi-stage Portfolio Selection Problems.pdf_P6-P10

西安交通大学博士学位论文 and the time series model. Based on the joint information framework, we define the regime-based time consistent nested risk measure. moreover we show how to establish and efficiently solve the corresponding multi-stage portfolio selection models by using the time consistent multi-period risk measure. We carry out a series of empirical tests to illustrate the superior performance of the proposed joint information framework and the corresponding multi-stage portfolio selection models (3)When an investor does not know the complete information about the distribution of the random loss, but only its moments information, we consider the distribution ally robust counterpart of the separate expectation conditional function, namely, the multi-period worst-case risk measure. By using the dynamic programming technique we derive the explicitly optimal investment strategy for the multi-stage robust portfo- lio selection problem under the multi-period worst-case risk measure. Numerical results demonstrate that the multi-period worst-case risk measure and the corresponding multi- stage portfolio selection model can help investors make robust decision to avoid extreme risks in worst-case scenarios (4)In more complex markets, not only the distribution of the random loss is unknown but its moments information is also unknown. To deal with the complex uncertainties in terms of both the distribution and the moments information, we propose two new uncertainty sets, and apply them to the multi-stage portfolio selection problems with the additive mean-CVar risk measure and the nested mean-CVar risk measure, respec tively. We find the closed form of the optimal portfolio or give an efficient solution method for these multi-stage robust portfolio selection problems. Numerical results il- lustrate that the robust mean-CVaR models with unknown moment information can steadily gain high returns and control extreme losses (5) To better describe the time-varying property of the multi-period investment risk with only partial information, we further propose two multi-period robust risk measures under the regime switching framework. We show that the corresponding multi-period robust portfolio selection problems under the regime dependent multi-period robust risk measures can be efficiently solved by using the scenario tree technique. Numerical results show the necessariness and efficiency of considering regime switching in multi-period ro- bust risk measures and multi-stage robust portfolio selection problems (6)For a class of investors who have pre-specified investment targets, we consider the effects of stochastic volatility on the time when the targets can be achieved. We define the earliest probabilistic target reaching time and propose a new risk measure which

‹SœåÆÆ¨Æ†ÿ© and the time series model. Based on the joint information framework, we define the regime-based time consistent nested risk measure. Moreover, we show how to establish and efficiently solve the corresponding multi-stage portfolio selection models by using the time consistent multi-period risk measure. We carry out a series of empirical tests to illustrate the superior performance of the proposed joint information framework and the corresponding multi-stage portfolio selection models. (3) When an investor does not know the complete information about the distribution of the random loss, but only its moments information, we consider the distributionally robust counterpart of the separate expectation conditional function, namely, the multi-period worst-case risk measure. By using the dynamic programming technique, we derive the explicitly optimal investment strategy for the multi-stage robust portfolio selection problem under the multi-period worst-case risk measure. Numerical results demonstrate that the multi-period worst-case risk measure and the corresponding multistage portfolio selection model can help investors make robust decision to avoid extreme risks in worst-case scenarios. (4) In more complex markets, not only the distribution of the random loss is unknown, but its moments information is also unknown. To deal with the complex uncertainties in terms of both the distribution and the moments information, we propose two new uncertainty sets, and apply them to the multi-stage portfolio selection problems with the additive mean-CVaR risk measure and the nested mean-CVaR risk measure, respectively. We find the closed form of the optimal portfolio or give an efficient solution method for these multi-stage robust portfolio selection problems. Numerical results illustrate that, the robust mean-CVaR models with unknown moment information can steadily gain high returns and control extreme losses. (5) To better describe the time-varying property of the multi-period investment risk with only partial information, we further propose two multi-period robust risk measures under the regime switching framework. We show that the corresponding multi-period robust portfolio selection problems under the regime dependent multi-period robust risk measures can be efficiently solved by using the scenario tree technique. Numerical results show the necessariness and efficiency of considering regime switching in multi-period robust risk measures and multi-stage robust portfolio selection problems. (6) For a class of investors who have pre-specified investment targets, we consider the effects of stochastic volatility on the time when the targets can be achieved. We define the earliest probabilistic target reaching time and propose a new risk measure which IV

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