Stochastic control on a long term and its applications

2015 Fiscal Year Final Research Report

• Project/Area Number: 25400150
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Kansai University
• Principal Investigator: NAGAI Hideo 関西大学, システム理工学部, 教授 (70110848)
• Co-Investigator(Renkei-kenkyūsha): Sekine Jun 大阪大学, 基礎工学研究科, 教授 (50314399) ; Takeda Masayoshi 東北大学, 理学研究科, 教授 (30179650) ; Ichihara Naoyuki 青山学院大学, 理工学部, 准教授 (70452563) ; Hata Hiroaki 静岡大学, 教育学部, 助教 (00609290)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: large deviation control / H-J-B equations / duality theorems / optimal consumption

Outline of Final Research Achievements

We have obtained certain duality theorems on large deviation estimates for controlled semi-martingales. Then, we have extended the results to the cases which correspond to the theorems for the robust large deviation estimates in actual financial models when admitting model unceratainty. Here, key analysis was that of the H-J-B equations of ergodic type and its derivatives for the corresponding dual problems, and by regarding them as the H-J-B equations of certain stochstic differential games, the estimates were obtained. On the other hand, we obtained the existence and uniqueness theorems for the solutions to the H-J-B equations of optimal consumption-investment, and verification theorems.

Free Research Field

確率論