数理ファイナンスセミナー

Math-Fi seminar on 10 Oct. (Co-organized as a Quantum Walk Seminar)

2024.10.08 Tue up
日時:2024年10月10日(木)16:30 〜 18:40

場所 :立命館大学BKCウエストウイング6階数理科学科談話会室&ZOOM

講演者1:高橋 佐良人 先生(テンソル・コンサルティング株式会社)

講演題目:量子ウォークとサポートの関係ーConnecting the Dotsー

講演要旨:
量子ウォークは,ランダムウォークの量子版として紹介されることが多いが,その挙動はランダムウォークとは大きく異なる。ランダムウォークでは確認できない量子ウォークの主な特徴として,線形的拡散と局在化(十分な時間が経過しても出発点に留まる性質) がよく知られているが,量子ウォークでは,有限なサポートが存在することも,大きな違いの一つとして認識されている。
本講演では,量子ウォークにおけるサポート,赤堀研と今野研の関係などを,「Connecting the Dots」というキーワードをもとに説明することを試みる。
 

講演者2:松岡 雷士 先生(広島工業大学)


講演題目:量子ウォーク迷路解法の理論と実装

講演要旨:
吸収ノードのある量子ウォークを利用して、迷路状ネットワークの最短経路を導出する手法について紹介する。
スタートとゴールのノードにセルフループを設置してグローバーウォークを時間発展させると、迷路内のスタートとゴールをつなぐルート上のノードにのみ振幅が残留し、最短経路が浮かび上がる。
本講演では手法の詳細と瀬川・大野による数学的な記述について紹介しつつ、本アルゴリズムを古典計算機上で高速実装するための経過について紹介する。

Math-Fi seminar on 3 Oct.

2024.10.03 Thu up
Date: 3 October (Thu)

Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)

Time: 16:30–18:00

Speaker: Taiho Wang (Baruch College) 

Title: Relative entropy-regularized robust optimal order execution under transient impact

Abstract: 
In this talk, we cast optimal liquidation under linear temporary and transient price impact as a relative entropy-regularized robust optimal control problem. The problem is formulated as to maximize a reward-risk functional associated with the order execution agent’s profit-and-loss of trading and the execution risk taking into account market’s liquidity and uncertainty over a class of absolutely continuous strategies. The problem is made into an entropy-regularized stochastic differential game and is solved by adopting the principle of dynamic programming, yielding that the value function of the differential game satisfies an entropy-regularized Hamilton-Jacobi-Isaacs (rHJI) equation. Under the assumption of aggregate exponential transient impact and Gaussian prior, the rHJI equation reduces to a matrix Riccati differential equation. Further imposing constancy of the corresponding coefficients, the matrix Riccati differential equation can be linearized, resulting in analytical expressions for optimal strategy and trajectory as well as the posterior distribution of market activity. The talk is based on a joint work with Xue Cheng and Meng Wang.

Math-Fi seminar on 26 Sep. (Co-organized as a Quantum Walk Seminar)

2024.09.25 Wed up
日時 :2024年9月26日(木)16:30 〜 18:40

場所 :立命館大学BKCウエストウイング6階数理科学科談話会室&ZOOM

講演者1:久保田匠 先生(愛知教育大学)

講演題目:Grover walk の周期性に関する最近の研究

講演要旨:
量子ウォークはランダムウォークの量子版として導入された数理モデルであり、確率論の枠を超えてグラフ理論、関数解析学、量子情報理論など幅広い分野と密接に関連して研究されている。周期性は量子状態がいくらかの時刻を経て初期状態に戻るという現象であり、特定のグラフにおいてのみ発生する珍しい現象である。本講演では、まず量子について物理的な背景を簡単に説明したうえで離散時間の1次元量子ウォークを導入する。次に、グラフ上の量子ウォークでは定番の Grover walk と、その周期性に関する基本的な結果を紹介する。最後に Grover walk の周期性に関する最近の研究成果や未解決問題を紹介する。



講演者2:渡邉 扇之介 先生(福知山公立大大学)

講演題目:高階多値多近傍セルオートマトンとその応用

講演要旨:
セルオートマトンとは1次元格子状にあるセルが離散値の状態をもち,ある規則に従って時間発展する離散力学系である. セルオートマトンは様々な現象を記述できるといわれているが,計算機の限界から多くの研究は「低い階層」のセルオートマトンを用いた実験的な研究であり,演繹的な研究も離散数学の道具が少ないため進んではいない. 本講演では,「高い階層」のセルオートマトンに対する実験的・演繹的アプローチを試みる. また,複数のセルオートマトンの確率的な組合せによって得られる確率モデルについても紹介する.

Math-Fi seminar on 19 Sep.

2024.09.18 Wed up
Date: 19th September (Thu)
Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
Time: 16:30–18:00

Speaker: Taiho Wang (Baruch College) 

Title:  Growth rate of wealth in G3Ms 

Abstract:
Geometric mean market makers (G3Ms), such as Uniswap and Balancer, represent a widely used class of automated market makers (AMMs). These G3Ms are characterized by the following rule: the reserves of the AMM must maintain the same (weighted) geometric mean before and after each trade. In this talk, we investigate the effects of trading fees on liquidity providers’ (LP) profitability in a G3M, as well as the adverse selection faced by LPs due to arbitrage activities involving a reference market. Our work expands previous models to G3Ms, integrating both transaction fees and continuous-time arbitrage into the analysis. Within this context, we analyze G3M dynamics, characterized by stochastic storage processes, and calculate the growth rate of LP wealth. We extend earlier results on constant product market maker, commonly referred to as Uniswap v2, as a special case. The talk is based on a joint work with Cheuk Yin Lee and Shen-Ning Tung.

Math-Fi seminar on 5 Sep

2024.08.30 Fri up
Date: 5th September (Thu)
Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
Time: 16:30–18:30

Speaker 1: Long Ngo Hoang (Laboratory of Applied Mathematics)
 
Title: Well-posedness, regularity of solutions and the $\theta$-Euler-Maruyama scheme for  stochastic Volterra integral equations with general singular kernels and jumps
 
Abstract: 
In this talk, we consider a class of stochastic Volterra integral equations with general singular kernels, driven by a Brownian motion and a pure jump L\’evy process. We first show that these equations have a unique strong solution under certain regular conditions on their coefficients. Furthermore, the solutions of this equation depend continuously on the initial value and on the kernels $k$, $k_B$, and $k_Z$. We will then show the regularity of solutions for these equations. Finally, we propose a $\theta$-Euler-Maruyama approximation scheme for these equations and demonstrate its convergence at a certain rate in the $L^2$-norm. 
This is a joint work with PHAN Thi Huong (Le Quy Don Technique University) and Peter Kloeden (Universit\”{a}t T\”{u}bingen)


Speaker 2: Tran Ngoc Khue (Hanoi University of Science and Technology) 

Title:On the infinite time horizon approximation for Lévy-driven McKean-Vlasov SDEs with non-globally Lipschitz continuous and super-linearly growth drift and diffusion coefficients

Abstract:  
This talk presents the study of the numerical approximation for McKean-Vlasov stochastic differential equations driven by Lévy processes. We propose a tamed-adaptive Euler-Maruyama scheme and consider its strong convergence in both finite and infinite time horizons when applying for some classes of Lévy-driven McKean-Vlasov stochastic differential equations with non-globally Lipschitz continuous and super-linearly growth drift and diffusion coefficients. This is a joint work with Hoang-Long Ngo, Duc-Trong Luong and Trung-Thuy Kieu.

Math-Fi seminar on 29 August

2024.08.22 Thu up
Date: 29th August (Thu)
Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
Time: 16:30–18:00
 
Speaker: Noriyoshi Sakuma (Nogoya City University)
 
Title: Fluctuations of eigenvalues of a polynomial on Haar unitary and finite rank matrices
 
Abstract:
In this talk, I will explain how to calculates the fluctuations of eigenvalues of polynomials on large Haar unitaries cut by finite rank deterministic matrices. When the eigenvalues are all simple, we can give a complete algorithm for computing the fluctuations.

Prob & Math-Fi seminar on 25 July

2024.07.24 Wed up
  • Date: 25 July (Thu.)
  • Place: W.W. 6th-floor, Colloquium Room and on the Web (Zoom)
  • Time: 15:30 – 18:30
  •  
  • Speaker 1: Daiki Tagami (Oxford University), 15:30-17:00
  • Title 1: tstrait: a quantitative trait simulator for ancestral recombination graphs
  • Abstract 1:
  • Ancestral recombination graphs (ARGs) encode the ensemble of correlated genealogical trees arising from recombination in a compact and efficient structure, and are of fundamental importance in population and statistical genetics. Recent breakthroughs have made it possible to simulate and infer ARGs at biobank scale, and there is now intense interest in using ARG-based methods across a broad range of applications, particularly in genome-wide association studies (GWAS). Sophisticated methods exist to simulate ARGs using population genetics models, but there is currently no software to simulate quantitative traits directly from these ARGs. To apply existing quantitative trait simulators users must export genotype data, losing important information about ancestral processes and producing prohibitively large files when applied to the biobank-scale datasets currently of interest in GWAS. We present tstrait, an open-source Python library to simulate quantitative traits on ARGs, and show how this user-friendly software can quickly simulate phenotypes for biobank-scale datasets on a laptop computer.
 
  • Speaker 2: Hau-Tieng Wu (NYU Courant Institute of Mathematical Sciences), 17:00-18:30
  • Title 2: Statistical Inference for Nonstationary Time Series via Phase-Driven Time-Frequency Analysis
  • Abstract 2:
  • Real-world time series are typically nonstationary and consist of multiple oscillatory components exhibiting complex statistical characteristics such as time-varying amplitude, frequency, and non-sinusoidal patterns. Signal quality is often compromised by intricate noise or artifacts. I will discuss recent advancements in addressing such time series using phase-driven nonlinear time-frequency analysis, highlighting recent statistical inference outcomes. Additionally, biomedical applications and unresolved mathematical challenges will be illustrated

Math-Fi seminar on 18 Jul. (Co-organized as a Quantum Walk Seminar)

2024.07.13 Sat up
  • 日時 :2024年7月18日(木)16:30 〜 18:00  
  • 場所 :立命館大学BKCウエストウイング6階数理科学科談話会室&ZOOM
  • 講演者 : 和田 和幸 氏(北海道教育大学 旭川校)
  • 講演題目   : 量子ウォークの離散固有値に付随する固有関数の指数減衰性
  • 講演要旨  :
 量子ウォークは古典ランダムウォークの量子力学版と称される数理モデルである.
 量子ウォークの固有値・固有関数を調べる事は重要である.
         シュレディンガー作用素の文脈では,無限遠方への指数減衰性は固有関数が持つ典型的な特徴の1つ           であると考えられている.
         1次元量子ウォークでは転送行列を用いる事で,直接固有ベクトルの無限遠方での挙動を見る事がで           きる(黄海-齋藤, 2021, QIPなど).
         講演では関数解析の視点から,いくつかの仮定を満たせば固有関数が無限遠方で指数減衰する事を
         紹介したい.
         この結果は,布田-船川-鈴木による多次元量子ウォークの結果(2017, QIP)に応用可能である.
         全体を通して1次元を例に取り,平易な言葉で解説を試みたい.
 

Math-Fi seminar on 11 July

2024.07.09 Tue up
  • Date: 11 July (Thu.)
  • Place: W.W. 6th-floor, Colloquium Room and on the Web (Zoom)
  • Time: 16:30 – 18:00

  • Speaker : Anna Aksamit(Usydney)    
  • Title: Introduction to robust finance Ⅲ
  • Abstract: 
  •  In this short course we present robust approach to pricing and hedging. The aim is to find bounds on the prices of exotic derivatives in terms of the (market) prices of call options. We do not make any explicit assumptions about the dynamics of the price process of the underlying asset. We deduct information about the distribution of asset prices from the call prices. The obtained bounds are robust with respect to model assumptions. We will present pricing and hedging of some specific payoffs, as well as, duality for more general class of payoffs

Math-Fi seminar on 4 July

2024.07.04 Thu up
  • Date: 4 July (Thu.)
  • Place: W.W. 6th-floor, Colloquium Room and on the Web (Zoom)
  • Time: 16:30 – 18:00

  • Speaker : Anna Aksamit(Usydney)    
  • Title: Introduction to robust finance Ⅱ
  • Abstract: 
 In this short course we present robust approach to pricing and hedging. The aim is to find bounds on the prices of exotic derivatives in terms of the (market) prices of call options. We do not make any explicit assumptions about the dynamics of the price process of the underlying asset. We deduct information about the distribution of asset prices from the call prices. The obtained bounds are robust with respect to model assumptions. We will present pricing and hedging of some specific payoffs, as well as, duality for more general class of payoffs