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

三浦良三：一直致力于利用等级信息的投资组合的理论和实证研究。他还处于股票规模效应随机过程的实证研究阶段，这对于研究等级投资组合的本质是至关重要的。沿着这一研究，他对股票价格的排名有了不同的看法，这种排名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的价格在同一只股票在预定时间间隔内的价格中的排名。他研究并推导出股票价格的概率分布。然后，他利用这一结果定价的一个新的异国情调的选择，命名为随机走廊选项，他在这个研究项目中创建。中村：我们研究了几个问题，涉及最优风险转移与一个新的证券创新从其发行人到投资者的基础上随机微分效用（SDU）。利用随机最大值原理，我们证明了两个代理人的最优风险转移，消费，投资政策的特点是由一个向前-向后随机微分方程组。此外，我们还探讨了不确定的时间范围，事件风险和模型risk.Izumi Nagayama基于SDU的最大化问题：她已经测试了基于Black-Scholes模型的模型风险对冲的有效性数值。她发现众所周知的vega-hedging并不总是很好，她还研究了原因。Shoji Kamimura：最近，Fujita和Miura（2006）给出了秩的概率分布的数学封闭形式。然而，这些封闭形式是如此复杂，我们无法看到或想象的数字形状的概率分布。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图形和性质。

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.