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Studies on Dynamic Optimization of Stochastic Systems with Multiple Criteria

多准则随机系统动态优化研究

基本信息

批准号：
10680427
负责人：
OHNISHI Masamitsu
金额：
$ 2.05万
依托单位：
Osaka University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1998
资助国家：
日本
起止时间：
1998 至 2000
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10680427/
关键词：
Optimal stopping problem Poisson process Geometric Brownian motion Smooth pasting Impulse control Risk aversion Stochastic dominance Multiple criteria Markov decision process 拡散過程配当政策キャッシュ・マネージメント確率優位(確率順序)信頼性・保全性投資意思決定マル

项目摘要

First, I examined an optimal stopping problem for a geometric Brownian motion with Poissonian jumps. Although it has been argued that so called smooth pasting technique (see Dixit (1993), and Dixit and Pindyck (1994)) is useful for such stochastic optimization problems, it seems that its mathematical validity is not sufficiently discussed so far. In this project, by taking a martingale approach, I showed that it is indeed mathematically valid under a set of some mild conditions on the parameters of the problem.Stochastic dominances (stochastic orders) and inequalities are very useful tools in various areas of economics and finance. The second purpose of this project was to describe main results obtained so far by using the idea of stochastic dominances in financial optimization. Especially, the emphasis is placed on the demand and shift effect problems in portfolio selection. Some other examples, which are not related directly to optimization problems, are also gathered to demonstrate the wide spectrum of application areas of stochastic dominances in finance. Further, since several stochastic dominances and related inequalities which are known in the reliability and maintainability theory, are very useful even in finance theory, the next purpose of this project was to provide a brief survey of the useful known results concerning stochastic orders and their applications developed in various areas of the reliability and maintainability theory.

首先，我研究了具有泊松跳跃的几何布朗运动的最佳停止问题。尽管有人认为所谓的平滑粘贴技术（参见 Dixit (1993) 以及 Dixit 和 Pindyck (1994)）对于此类随机优化问题很有用，但迄今为止其数学有效性似乎尚未得到充分讨论。在这个项目中，通过采用鞅方法，我证明了在问题参数的一些温和条件下，它确实在数学上是有效的。随机优势（随机阶）和不平等在经济和金融的各个领域都是非常有用的工具。该项目的第二个目的是描述迄今为止在金融优化中使用随机优势思想所获得的主要结果。特别是，重点关注投资组合选择中的需求和转移效应问题。还收集了一些与优化问题没有直接关系的其他示例，以展示随机优势在金融领域的广泛应用领域。此外，由于可靠性和可维护性理论中已知的几种随机优势和相关不等式甚至在金融理论中也非常有用，因此该项目的下一个目的是对有关随机阶的有用的已知结果及其在可靠性和可维护性理论的各个领域中开发的应用进行简要调查。