传统的风险控制以终端财富的各阶中心矩作为风险度量，而现在越来越多的投资模型转向以不对称的在某个特定临界值的下行风险作为风险度量。在现有的下行风险中，安全第一准则，风险价值，条件风险价值，下偏矩可能是最有活力的代表。在这篇博士论文中，在已有的静态文献之上，我们讨论了以安全第一准则，风险价值，条件风险价值，下偏矩为风险度量的一系列动态投资组合问题。我们的贡献在于两个方面，一个是建立了可以被解析求解的模型，另一个是得到了最优的投资策略。在终端财富上加上一个上界，使得我们克服了一类下行风险投资组合问题的不适定性。引入的上界不仅仅使得我们的下行风险下的投资组合问题能得到显式解，而且也让我们可以控制下行风险投资组合问题的最优投资的冒险性。用分位数法和鞅方法，我们能够得到上述的各种模型的解析解。在一定的市场条件下，我们得到了对应的拉格朗日问题的乘子的存在性和唯一性, 这也是对应的鞅方法中的核心步骤。更进一步，当市场投资组合集是确定性的时候，我们推出解析的最优财富过程和最优投资策略。 / Instead of controlling "symmetric" risks measured by central moments of terminal wealth, more and more portfolio models have shifted their focus to manage "asymmetric" downside risks that the investment return is below certain threshold. Among the existing downside risk measures, the safety-first principle, the value-at-risk (VaR), the conditional value-at-risk (CVaR) and the lower-partial moments (LPM) are probably the most promising representatives. / In this dissertation, we investigate a general class of dynamic mean-downside risk portfolio selection formulations, including the mean-exceeding probability portfolio selection formulation, the dynamic mean-VaR portfolio selection formulation, the dynamic mean-LPM portfolio selection formulation and the dynamic mean-CVaR portfolio selection formulation in continuous-time, while the current literature has only witnessed their static versions. Our contributions are two-fold, in both building up tractable formulations and deriving corresponding optimal policies. By imposing a limit funding level on the terminal wealth, we conquer the ill-posedness exhibited in the class of mean-downside risk portfolio models. The limit funding level not only enables us to solve dynamic mean-downside risk portfolio optimization problems, but also offers a flexibility to tame the aggressiveness of the portfolio policies generated from the mean-downside risk optimization models. Using quantile method and martingale approach, we derive optimal solutions for all the above mentioned mean-downside risk models. More specifically, for a general market setting, we prove the existence and uniqueness of the Lagrangian multiplies, which is a key step in applying the martingale approach, and establish a theoretical foundation for developing efficient numerical solution approaches. Furthermore, for situations where the opportunity set of the market setting is deterministic, we derive analytical portfolio policies. / Detailed summary in vernacular field only. / Zhou, Ke. / Thesis (Ph.D.) Chinese University of Hong Kong, 2014. / Includes bibliographical references (leaves i-vi). / Abstracts also in Chinese.
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_1077694 |
| Date | January 2014 |
| Contributors | Zhou, Ke (author.), Li, Duan , 1952- (thesis advisor.), Chinese University of Hong Kong Graduate School. Division of Systems Engineering and Engineering Management, (degree granting institution.) |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography, text |
| Format | electronic resource, electronic resource, remote, 1 online resource (x, 113, vi leaves) : illustrations, computer, online resource |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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