ANALYSIS ON DYNAMICAL DECISION MAKING UNDER UNCERTAINTY AND ITS APPLICATIONS

本研究的目的是分析不确定性下模糊决策过程的数学结构及其在金融工程中的应用。主要结果如下。（i）研究了不确定（随机和模糊）环境中的最优停止过程。（ii）分析了具有感知的马尔可夫决策过程的模糊处理。（iii）零和游戏停止/决策模糊系统的发展。（4）研究了不确定环境下模糊决策问题中带停时和序的多目标决策问题。（v）针对这些应用，建立了不确定环境下的美式和欧式期权模型。得到了不确定环境下期权价格的可靠性区间。投资组合问题也是在同样的条件下发展起来的。（vi）讨论了具有模糊偏好的估计和决策问题，这些结果发表在Springer和比尔克的讲座笔记系列中 ...更多信息 豪瑟和下列国际期刊：模糊集和系统，信息科学，欧洲运筹学杂志，数学分析。应用程序、非线性凸分析，数学与计算机建模，计算机与数学应用，我们还在以下国际会议和研讨会上发表了一些成果：SCI 2001（美国奥兰多），IFSA/NAFIPS 2001（加拿大温哥华），NACA 2001（广崎），FSS 2001（东京），KES 2001（大坂），INFORMS 2001（Miamiin USA），FUZZ-IEEE 2001（澳大利亚墨尔本）、MOPGP 2002（奈良）、IPMU 2002（法国阿讷西），IFORS 2002年（爱丁堡），OSSG 2002（波兰的Bedlewoin），NGRA 2002（俄罗斯彼得罗扎沃茨克），公元前9年（中国北京），NACA 2002（广崎），SMPS 2002（波兰华沙），KES 2002（意大利的克雷马），风险SM 2002（法国夏蒙尼），FSKD 2002（新加坡），IFSA 2003（土耳其伊斯坦布尔），2003年欧洲/信息（土耳其的伊斯坦布尔）、NACA 2003（东京）、FUBUTEC 2004（法国枫丹白露），IPMU 2004（意大利佩鲁贾），FUZZ-IEEE 2004（匈牙利布达佩斯），MDAI 2004（西班牙巴塞罗那），KES2004（新西兰的惠灵顿）等。我们每年还在北九州大学或千叶大学举办研讨会。在这项研究中，本文分析了不确定动态系统决策的数学结构，并给出了它在经济学、管理科学和金融工程决策中的应用。我们感谢几位教授对本课题的支持：E.E.Kerre教授（比利时根特大学）、J.Kacprzyk教授（波兰科学院）、M.Sniedovich教授（澳大利亚墨尔本大学）等。少

The aim of this research is analysis of the mathematical structure of fuzzy decision processes under uncertainty and its application to financial engineering. The main results are as follows.(i)Optimal stopping processes in uncertain (stochastic and fuzzy) environments are studied.(ii)Fuzzy treatments of Markov decision processes with perception are analyzed.(iii)Zero-sum games regarding stopping/decision making in fuzzy systems are developed.(iv)Multi-object decision making with stopping times and ordering in decision-making problems under fuzziness are discussed in uncertain environments.(v)For these applications, American and European option models in uncertain environments are established. The reliability intervals of option prices in uncertain environments are obtained. Portfolio problems are also developed under the same conditions.(vi)Estimation and decision making with fuzzy preferences are discussed.These results are published by books Lecture Notes series in Springer and Birk … More hauser and by the following international journals: Fuzzy Sets and Systems, Information Sciences, European Journal of Operational Research, J. Math. Anal. Appl., J. Nonlinear Convex Analysis, Math. and Comp. Modelling, Comp. & Math. Appl., Fuzzy Optimization and Decision Making and so on. We have also presented some results at the following international conferences and workshops: SCI 2001 (Orlando in USA), IFSA/NAFIPS 2001 (Vancouver in Canada), NACA 2001 (Hirosaki), FSS 2001 (Tokyo), KES 2001 (Osaka), INFORMS 2001 (Miamiin USA), FUZZ-IEEE 2001 (Melbourne in Australia), MOPGP 2002 (Nara), IPMU 2002 (Annecy in France), IFORS 2002 (Edinburgh), OSSG 2002 (Bedlewoin in Poland), NGRA 2002 (Petrozavodsk in Russia), 9BC (Beijin in China), NACA 2002 (Hirosaki), SMPS 2002 (Warsaw in Poland), KES 2002 (Crema in Italy), Risk SM 2002 (Chamonix in France), FSKD 2002 (Singapore), IFSA 2003 (Istanbul in Turkey), EURO/INFORMS 2003 (Istanbul in Turkey), NACA 2003 (Tokyo), FUBUTEC2004 (Fontainebleau in France), IPMU2004 (Perugia in Italy), FUZZ-IEEE 2004 (Budapest in Hungary), MDAI2004 (Barcelona in Spain), KES2004 (Wellington in New Zealand) and so on. We have also held a workshop every year in the University of Kitakyushu or Chiba University.In this research, we have analyzed the mathematical structure of decision making on dynamic systems under uncertainty and we have obtained its application to decision making in economics, management science and financial engineering. We appreciate for several professor's support to this topic : Prof.E.E.Kerre (Ghent University in Belgium), Prof.J.Kacprzyk (Polish Academy of Sciences), Prof.M.Sniedovich (University of Melbourne in Australia) etc.. Less