2018年度

Math-Fi seminar on 20 Sep.

2018.09.18 Tue up
  • Date: 20 Sep. (Thu.)
  • Place: W.W. 6th-floor, Colloquium Room
  • Time: 16:30-18:00
  • Speaker: Libo Li (University of New South Wales)
  • Title: On a positivity preserving numerical scheme for jump-extended CIR process: the alpha-stable case
  • Abstract:
​We propose a positivity preserving implicit Euler-Maruyama scheme for a jump-extended Cox-Ingersoll-Ross (CIR) process where the jumps are governed by compensated spectrally positive alpha-stable process for alpha belonging to (1,2). Different to the existing positivity preserving numerical schemes for jump-extended CIR or CEV models, the model considered here has infinite activity jumps. We calculate, in this specific model, the strong rate of convergence and give some numerical illustrations. Jump extended models of this type were initially studied in the context of branching processes and was recently introduced to the financial mathematics literature to model sovereign interest rates, power and energy markets.
 

Math-Fi seminar on 13 Sep.

2018.09.10 Mon up
  • Date: 13 Sep. (Thu.)
  • Place: W.W. 6th-floor, Colloquium Room
  • Time: 15:00-18:00
  • Speaker: Libo Li (University of New South Wales)
  • Title: multivariate analysis

Math-Fi seminar on 11 Sep.

2018.09.10 Mon up
  • Date: 11 Sep. (Tue.)
  • Place: W.W. 6th-floor, Colloquium Room
  • Time: 14:00-
  • Speaker: Arturo Kohatsu-Higa (Ritsumeikan University)
  • Title: regression analysis

Math-Fi seminar on 30 Aug.

2018.08.29 Wed up
  • Date: 30 Aug. (Thu.)
  • Place: W.W. 6th-floor, Colloquium Room
  • Time: 16:30-18:00
  • Speaker: Makoto Yamazato (Tokyo Woman’s Christian University)
  • Title: Boundedness of the densities of CME-subordinators
 

Math-Fi seminar on 23 Aug.

2018.08.20 Mon up
  • This seminar was canceled.　　

Math-Fi seminar on 26 Jul.

2018.07.12 Thu up
  • Date: 26 Jul. (Thu.)
  • Place: W.W. 6th-floor, Colloquium Room
  • Time: 16:30-18:00
  • Speaker: Xiaoshan Su (EMLYON Business School)
  • Title: Some interesting insurance work: Distribution Choice in Non-life Insurance Risk Model with Statistical Learning Method & Optimal Insurance under Third Degree Risk
(Xiaoshan Su emlyon business school)
  • Abstract: 
​The former work treats a distribution selection problem as a classification problem for claim frequency and claim severity in non-life insurance risk model, and trains machine learning classifier to predict most likely distribution for real data. The training of classifier uses a simulation training sample that is generated under a two-level hierarchical structure. The first level is to generate enough pieces of parameter sets for all competitive distributions, and for each piece of parameter set in each distribution, the second level is to simulate a large size of sample and compute the respective values of descriptive statistic variables, which forms a record of training sample by combination with the corresponding distribution label. Then, the cross-validation method compares the performance of commonly used classifiers, including decision tree, k-nearest neighbour classifier, neural network, support vector classifier, bagging, boosting and random forest, etc. Both of numerical experiments and empirical studies show decision tree and bagging, boosting and random forest that use decision tree as weak learners, perform better than other classifiers and also than traditional fitting measures. The latter work investigates the optimal insurance design of considering a wide coverage of insured including risk-averter and risk-lovers, by assuming that the insured is third degree risk averse. Under expected value premium principle, we show that the optimal insurance form is a change-loss insurance or a dual change-loss insurance, which depends on the coefficient-variance of the ceded loss. The insurer with a mean-variance preference has a strong motive to issue these two kinds of insurance contracts.

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。

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