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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，我研究了一个最佳停止问题的几何布朗运动的泊松跳跃。虽然有人认为，所谓的光滑粘贴技术（见Diplomat（1993），Diplomat和Pindyck（1994））是有用的，这样的随机优化问题，它似乎没有充分讨论到目前为止，其数学有效性。在这个项目中，通过采用鞅方法，我证明了它确实是数学上有效的一组温和的条件下的参数的问题。随机优势（随机订单）和不等式是非常有用的工具，在经济和金融的各个领域。本项目的第二个目的是描述迄今为止通过使用金融优化中的随机优势的思想所获得的主要结果。特别是，重点放在需求和转移效应的投资组合选择问题。一些其他的例子，这是不直接相关的优化问题，也收集到展示金融随机优势的广泛应用领域。此外，由于几个随机优势和相关的不平等，这是已知的可靠性和维修性理论，是非常有用的，甚至在金融理论，该项目的下一个目的是提供一个简短的调查有关的有用已知的结果随机订单和它们的应用开发在各个领域的可靠性和维修性理论。