Mathematical Decision Analysis and its Application to Economic Theory

2019 Fiscal Year Final Research Report

• Project/Area Number: 16K05282
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: The University of Kitakyushu
• Principal Investigator: Yoshida Yuji 北九州市立大学, 経済学部, 教授 (90192426)
• Project Period (FY): 2016-04-01 – 2020-03-31
• Keywords: 数理ファイナンス / リスク / 効用 / 不確実性 / 意思決定

Outline of Final Research Achievements

Stochastic dominance and risk premiums on two-dimensional regions are studied by weighted quasi-arithmetic means. A necessary condition and a sufficient condition for risk averse comparison of two utility functions are also given.
Minimizing the distance between risk estimations through decision maker's utility and coherent risk measures with risk spectra is discussed, and the risk spectrum of the optimal coherent risk measures is obtained and it inherits the risk averse property of utility functions. In Markov decision processes, risk-sensitive expected 　rewards under utility functions are approximated by weighted average value-at-risks, and risk constraints are described by coherent risk measures with the best risk spectrum derived from decision maker's risk averse utility. The mathematical optimality methods in Markov decision making are obtained for high-speed calculation in financial engineering.

Free Research Field

数理的決定過程

Academic Significance and Societal Importance of the Research Achievements

近年は、金融不安や地震災害など様々なリスクの中で、安定した社会基盤を築くことが求められている。リスクは不確実性と深くかかわり、リスクの数学的性質は心理学や経済学など様々な分野で研究されてきた。本研究では、経済や災害のリスク環境における意思決定の解析的性質を数理計画の観点から考察する。とくに、リスクを伴う確率場と意思決定者の評価基準の相互関係について数理的モデルを用いて研究する。また、社会や経済におけるリスクの連鎖も研究目的とし、ダイナミックスを伴うリスク環境における意思決定の解析的推移を数理計画の観点から研究する。