大阪大学　数理・データ科学教育研究センター
Center for Mathematical Modeling and Data Science,Osaka University

Topics in Mathematical Finance II

Kostas Kardaras (Boston), 高岡浩一郎（一橋大学）, 貝瀬秀裕（名古屋大学）

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4. Topics in Mathematical Finance II

One Day Seminar

Topics in Mathematical Finance II

Kostas Kardaras (Boston), 高岡浩一郎（一橋大学）, 貝瀬秀裕（名古屋大学）

14:00--15:30, Kostas Kardaras (Boston)
title: "Arbitrage of the first kind and the structure of wealth processes"
abstract:
In this talk, the relationship between absence of arbitrage of the first kind in the market, existence of strictly positive supermartingale deflators and the semimartingale property of discounted asset prices in frictionless financial modeling is explored. The setting will be quite abstract in the beginning in order to state general results. Subsequently, more specialized models will be considered, where sharper results can be obtained.

15:30--17:00, Koichiro Takaoka (Hitotsubashi) /高岡浩一郎（一橋大学）
title: "On the condition of no unbounded profit with bounded risk."
abstract:
As a simple corollary to Delbaen and Schachermayer's fundamental theorem of asset pricing (1994) (1995) (1998), we prove, in a general d-dimensional semimartingale setting, that the no unbounded profit with bounded risk (NUPBR) condition is equivalent to the existence of a strict martingale density for the price process. We do not assume the path continuity nor the positivity of the price process. This extends the result of Choulli and Stricker (1996) to the cadlag cases, and refines partially the second main result of Karatzas and Kardaras (2007) concerning the existence of an equivalent supermartingale deflator.

17:00--18:30, Hidehiro Kaise (Nagoya)/ 貝瀬秀裕（名古屋大学）
title: "H-infinity control of differential game and its application to investment problems"
abstract:
H-infinity control is a robust control theory where problems are formulated as zero-sum games between a controller and an unknown deterministic disturbance. Since H-infinity control can be formally obtained by small noise limit and risk-averse limit of risk-sensitive control, we can consider H-infinity control-type formulations of financial problems. In this talk, we review basic ideas and results on H-infinity control of differential games. As applications to mathematical finance, we discuss optimal investment problems in the framework of H-infinity control.