数理ファイナンスセミナー

Math-Fi seminar on 19 Jul.

2018.07.10 Tue up
  • Date: 19 Jul. (Thu.)
  • Place: W.W. 6th-floor, Colloquium Room
  • Time: 15:30-16:30 (First speaker), 16:30-17:30 (Second speaker), 17:30-19:00 (Third speaker) 
 

　First speaker: Xiaoshan Su (EMLYON Business School)
  • Title: Pricing Defaultable Participating Contracts with Regime Switching and Jump Risk
(Xiaoshan Su emlyon business school Joint work with Professor Olivier Le Courtois and Professor Francois Quittard Pinon)
  • Abstract:
This paper provides a regime switching jump diffusion framework for pricing defaultable participating life insurance contracts. This framework assumes the value of underlying asset portfolio evolves as a geometric regime switching double exponential jump diffusion and default happens when its value crosses a level with regard to initial policyholder premium. The flexible regime switching double exponential jump diffusion model gives the semi-closed form formula for the price of the life insurance contract and the price can be obtained by further computation using numerical two-sided Laplace inversion method. The Euler summation technique is used to speed up the convergence rate of two-dimensional Laplace inversion method in Cai and Shi (2015) and the ”worst state” is defined to help control the discretion and truncation errors of numerical two-sided Laplace inversion in the regime switching case. An illustration concludes the paper and addresses the respective impacts of different risk sources on the price of the life insurance contracts.


 
　Second speaker: Arturo Kohatsu-Higa (Ritsumeikan University)
  • Title: The fundamentals of the ibp formula
     
 
　Third speaker: Linghua Chen (Analyst; Greenfact AS, Oslo, Norway)
  • Title: Numerical path integration methods to SDEs and applications

Math-Fi seminar on 12 Jul.

2018.07.10 Tue up
  • Date: 12 Jul. (Thu.)
  • Place: W.W. 6th-floor, Colloquium Room
  • Time: 16:30-18:00
  • Speaker: Xiaoshan Su (EMLYON Business School)
  • Title: Structural Pricing of CoCos and Deposit Insurance with Regime Switching and Jumps​
​(Xiaoshan Su emlyon business school Joint work with Professor Olivier Le Courtois)
  • Abstract:
In this article, we construct a structural model with jumps and regime switching to price banks’ contingent convertible debt (CoCos) and deposit insurance. We use an Esscher transform that is applicable to regime switching double exponential jump diffusions to move from the historical world to the risk-neutral world. Further, we define and implement a matrix Wiener-Hopf factorization associated with the latter processes, allowing us to price the various components of a bank’s balance sheet. Thus, we obtain valuation formulas for the bank’s equity, debt, deposits, CoCos, and deposit insurance. We also show in an illustration the respective effects of the jump risk and of regime switching on the values of all of a bank’s balance sheet components.

Math-Fi seminar on 28 Jun.

2018.06.26 Tue up
  • Date: 28 Jun. (Thu.)
  • Place: W.W. 6th-floor, Colloquium Room
  • Time: 16:30-18:00
  • Speaker: Takahiro Tsuchiya (University of Aizu)
  • Title: Newton-Kantorovitch method for non-Markov and decoupled forward-backward stochastic differential equations
  • Abstract:
Newton 法はよく知られているように滑らかな実数値関数$f$ について $ f(x)=0 $ を満たす解 $x$の近似列の構成を明示的に与える．
その近似列の well-defined および，解への収束は Kantorovitchによって特徴づけられ，さらに一般の Banach 空間に値を取る作用素 にまで拡張された．
そして常微分方程式への応用は Chaplyginが行い，Vidossichが整備している．
加えて確率微分方程式への拡張，さらにその収束が時刻に関して一様であることは川端山田によってはじめて示された．
後ろ向きの方程式が絡む forward-backward stochastic differential equations (FBSDEs)では解の可解性は局所的に与える，
もしくは特定の条件を付与する必要があり，多くの貢献があるにもかかわらず，十分に解明されたというのは言い難い状況にある．
本講演ではランダムな係数を持つ decoupled FBSDEs における Newton-Kantorovitch法の構成と一様収束について報告する．
 

Math-Fi seminar on 14 Jun.

2018.06.11 Mon up
  • Date: 14 Jun. (Thu.)
  • Place: W.W. 6th-floor, Colloquium Room
  • Time: 16:30-18:00
  • Speaker: Ryuya Namba (Okayama University)
  • Title: A functional central limit theorem for non-symmetric random walks on nilpotent covering graphs
  • Abstract:
べき零群を被覆変換群とするような有限グラフの被覆グラフのことを
べき零被覆グラフと呼ぶ。結晶格子(被覆変換群がアーベル群の場合)
上のランダムウォークに関しては既に多くの極限定理が離散幾何解析
の枠組みで得られている。本講演では、べき零被覆グラフ上の非対称
ランダムウォークを考察し汎関数中心極限定理を考察し、スケール極限
として捉えたあるべき零Lie群値の拡散過程に、ランダムウォークの
非対称性からくるドリフト項が現れることを報告する。また、この
ドリフト項がグラフの実現写像のambiguityによらず定まるという
驚くべき事実も得たので、これについても講演内で触れる予定である。
時間が許せば、ラフパス理論との関連および証明の概略についても
話したい。本講演の内容は、石渡 聡氏(山形大)および河備 浩司氏(慶應大)
との共同研究に基づく。

Math-Fi seminar on 7 Jun.

2018.06.04 Mon up
  • Date: 7 Jun. (Thu.)
  • Place: W.W. 6th-floor, Colloquium Room
  • Time: 16:30-18:00
  • Speaker: Jiro Akahori (Ritusmeikan University)
  • Title:  An Introduction to Discrete Stochastic Calculus

Math-Fi seminar on 31 May

2018.05.29 Tue up
  • Date: 31 May (Thu.)
  • Place: W.W. 6th-floor, Colloquium Room
  • Time: 16:30-18:00
  • Speaker: Daisuke Shiraishi (Kyoto University)
  • Title: Natural parametrization for loop-erased random walk in three dimensions

Math-Fi seminar on 24 May

2018.05.21 Mon up
  • Date: 24 May (Thu.)
  • Place: W.W. 6th-floor, Colloquium Room
  • Time: 16:30-18:00
  • Speaker: Benjamin Poignard (Osaka University)
  • Title: Non-Asymptotic Properties of Regularized Multivariate ARCH models
  • Abstract:
We provide finite sample properties of regularized multivariate ARCH processes, where the linear representation of ARCH models allows for an ordinary least square estimation. Under the restricted strong convexity of the unpenalized loss function, regularity conditions on the regularizer, strict stationary and beta-mixing process, we prove non-asymptotic error bounds on the regularized ARCH estimators. Moreover, based on the primal-dual witness method, we establish variable selection consistency, including the case when the regularizer is non-convex. These theoretical results are supported by simulation studies. 

Math-Fi seminar on 26 Apr.

2018.04.26 Thu up
  • Date: 26 Apr. (Thu.)
  • Place: W.W. 6th-floor, Colloquium Room
  • Time: 16:30-18:00
  • Speaker: Keita Owari (Ritsumeikan University)
  • Title: Introduction to Duality Theory for Locally Convex Spaces
 

Math-Fi seminar on 19 Apr.

2018.04.16 Mon up
  • Date: 19 Apr. (Thu.)
  • Place: W.W. 6th-floor, Colloquium Room
  • Time: 16:30-18:00
  • Speaker: Giulia Livieri (SNS Pisa)
  • Title: Statistical inference for price staleness
  • Abstract:
Asset prices recorded at a high frequency are more sluggish than implied by the semi-martingale hypothesis. 
We propose a new general framework formalizing this phenomenon. We provide a limit theory for Idle-time (an economic indicator for price flatness) and related quantities. This allows to quantify the level of staleness in an asset price adjustment and to test two different hypothesis. First, whether the extent of sluggishness is constant or time-varying. Second, whether the sluggishness is persistent. The empirical application on US stocks provides the evidence that stock price flatness is both time-varying and persistent, especially during the crisis.
 

Math-Fi seminar on 12 Apr.

2018.04.09 Mon up
  • Date: 12 Apr. (Thu.)
  • Place: W.W. 6th-floor, Colloquium Room
  • Time: 16:30-18:00
  • Speaker: Yuuki Semba (Ritsumeikan Univeristy)
  • Title: Reinforced Random Walk
 

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