Theoretical Research on the problem of dynamic portfolio selection based on new approaches and Its Application

Miura Ryozo：他一直在对利用排名信息的投资组合进行理论和实证研究。他还处于对股票规模效应随机过程的实证研究阶段，这是研究等级投资组合的性质所必需的。伴随着这项研究，他对股票价格的排名也有了不同的看法，这不是一只股票在许多股票中的排名，而是一只股票在预定时间段内的价格在同一股票的价格中的排名。他研究并推导了股票价格的这个等级的概率分布。然后利用这一结果对他在本研究项目中创建的一种名为随机走廊期权的新的奇异期权进行定价。Nakamura：我们基于随机微分效用(SDU)研究了与新的证券创新从发行人到投资者的最优风险转移相关的几个问题。利用随机极大值原理，我们证明了两个代理人的最优风险转移、消费和投资策略都是由一个向前向后的随机微分方程组刻画的。此外，我们还研究了具有不确定时间范围、事件风险和模型风险的基于SDU的最大化问题。Izumi Nagayama：她对基于Black-Scholes模型的模型风险对冲的有效性进行了数值测试。她发现，众所周知的织女星对冲并不总是奏效的，她还检查了原因。她正在努力寻找套期保值模型风险的新方法。神村正治：最近，Fujita和Miura(2006)给出了序列概率分布的数学封闭形式。然而，这些封闭的形式是如此复杂，以至于我们看不到或想象不到概率分布的图形形状。然后，我们给出了一些数值结果，以了解这些秩统计量分布族的数字和性质。

Miura Ryozo: He has been working on Theoretical and empirical study on portfolios which utilize rank information. He is still on the stage of empirical study on size effect stochastic process of stocks, which is most essential in order to study the nature of the rank portfolio. Along with this study, he took a different look at the rank of stock prices which is not the rank of a stock among many stocks, but the rank of the price of a stock at a prefixed time among the prices of the same stock during a prefixed time interval. He has studied and derived a probability distribution of this rank of a price of a stock. Then he utilized this result for pricing of a new exotic option, named Stochastic Corridor Option, which he created during this research project.Nobuhiro Nakamura: We study several issues involving optimal risk transfer associated with a new security innovation from its issuer to investors based upon a stochastic differential utility (SDU). Using the stochastic maximum principle we have shown that the optimal risk transfer, consumptions, investment policies of both agents are characterized by a forward-backward stochastic differential equation system. Furthermore we have explored the SDU-based maximization problems with an uncertain time horizon, event risk and model risk.Izumi Nagayama: She has tested numerically for the effectiveness of model-risk-hedging based on the Black-Scholes model. She found out that the well-known vega-hedging does not always work well and she also examined the reason. She is trying to find the new way of hedging the model risk.Shoji Kamimura: Recently, Fujita and Miura(2006) have provided mathematical closed forms for the probability distribution of the rank. However, these closed forms are so complicated that we can not see or imagine the figure shape of the probability distribution. Then we have shown some numerical results to see the figures and properties of these family of distributions of the rank statistics.