Development of New Methods for Financial Market Risk Management based on a SoftApproach

本研究采用近年来首席研究员倡导的软方法，解决了以风险价值（VaR）衡量市场风险的金融投资模型，从而为市场风险管理提供了一种新的途径。提出了投资组合动态管理的两种模型，并给出了它们的解析方法。此外，我们还利用纽约证券交易所市场的真实股票价格数据进行了投资组合选择仿真和动态投资组合管理仿真，验证了所提出模型和方法的有效性。具体而言，本研究探讨了金融投资风险管理中的以下几个问题。(1)投资组合选择：提出了一种以VaR衡量市场风险的投资组合优化模型的求解方法。本文还对从多个角度衡量市场风险的投资组合问题进行了建模，并给出了解决方法。(2)投资组合再平衡：以资本利得税和交易佣金作为再平衡成本，构建了投资组合再平衡问题的优化模型。并给出了求解这些模型的软方法。(3)动态项目组合管理：提出了两种动态管理项目组合的模型。一种是预先确定再平衡时间的多阶段投资组合优化模型，另一种是再平衡时间不固定的控制理论模型。给出了求解这些模型的软方法。

This research solved the models built for financial investment with market risk measured by the Value at Risk (VaR), by using the soft approach that the head investigator has been advocating in recent years, thus provided a new way for managing market risk. And two models were proposed for managing portfolio dynamically, and their resolution methods were also provided. Furthermore, we demonstrated the validity of the proposed models and methods by conducting portfolio selection simulation and dynamic portfolio management simulation with real stock price data from the New York Stock Exchange market.Concretely, the research investigated the following issues concerned with risk management in financial investment.(1) Portfolio Selection : We gave a method for solving the portfolio optimization models with market risk measured by VaR using the soft approach. We also modeled the portfolio selection problems where market risk is measured from multiple views, and gave the resolution methods.(2) Portfolio Rebalancing : We built optimization models for portfolio rebalancing problems by taking capital gain tax and transaction commission as rebalancing cost. And soft methods for solving these models were also given.(3) Dynamic Portfolio Management : We proposed two models for managing portfolios dynamically. One is a multistage portfolio optimization model where rebalancing times are fixed in advance, while the other is a control-theoretical model where rebalancing times are not fixed. Soft methods for solving these models were provided.