Abstracts of Scheduled Seminars
Abstracts of Scheduled Seminars
(Probability and Mathematical Finance Seminar)
(Probability and Mathematical Finance Seminar)
Note: Dinner will be served to participants as the discussion part covers the dinner time.
Speaker: Noriyoshi Sakuma (Nagoya 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.
Speaker 1: Long Ngo Hoang (Laboratory of Applied Mathematics)
Speaker 2: Tran Ngoc Khue (Hanoi University of Science and Technology)
LONG Title: Well-posedness, regularity of solutions and the $\theta$-Euler-Maruyama scheme for stochastic Volterra integral equations with general singular kernels and jumps
TRAN 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
LONG 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)
TRAN 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.
Speaker: Taiho Wang (CUNY, 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.
Note: Dinner will be served to participants as the discussion part covers the dinner time.
Speaker: Taiho Wang (CUNY, 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
Speaker: Jorge Gonzalez-Cazares（UNAM)
Title: Markov Chain Monte Carlo: how and why?
Abstract: We will review classical and widely used Markov Chain Monte Carlo (MCMC) methods. We will begin by reviewing Markov Chain theory and posing the MCMC problem. We motivate the problem from the point of view of stochastic optimisation problems arising in statistics and machine learning. We introduce Metropolis Hastings and Gibbs samplers and show its simplicity using code. We will also hint at its connections with the popular SGD algorithm.
Speaker 1: Jorge Gonzalez-Cazares（UNAM), 16:30--17:00
Title 1: Markov Chain Monte Carlo: how and why? II
Abstract 1: We will review classical and widely used Markov Chain Monte Carlo (MCMC) methods. We will begin by reviewing Markov Chain theory and posing the MCMC problem. We motivate the problem from the point of view of stochastic optimisation problems arising in statistics and machine learning. We introduce Metropolis Hastings and Gibbs samplers and show its simplicity using code. We will also hint at its connections with the popular SGD algorithm.
Speaker 2: Andrea Macrina (University College London), 17:40–18:40
Title 2: Continuous-Time Quantile Processes with Applications in Finance and Insurance
Abstract 2: We develop a novel approach for the construction of quantile processes governing the stochastic dynamics of quantiles in continuous time. Two classes of quantile diffusions are identified: the first, which we largely focus on, features a dynamic random quantile level that allows for direct interpretation of the resulting quantile process characteristics such as location, scale, skewness, and kurtosis, in terms of the model parameters. The second type are function--valued quantile diffusions and are driven by stochastic parameter processes, which determine the entire quantile function at each point in time. By the proposed construction method, quantile processes are obtained by transforming the marginals of a diffusion process under a composite map consisting of a distribution and a quantile function. Sub-classes of quantile diffusions are explored, with emphasis placed on the Tukey family of models whereby skewness and kurtosis are directly parameterised and thus the composite map is explicable with respect to such statistical behaviours. As an example of an application of quantile diffusions, we show how probability measure distortions, a form of dynamic tilting, can be induced. Though particularly useful in financial mathematics and actuarial science, examples of which are given in this work, measure distortions feature across multiple research areas. For instance, dynamic distributional approximations (statistics), non-parametric and asymptotic analysis (mathematical statistics), dynamic risk measures (econometrics), behavioural economics, decision making (operations research), signal processing (information theory), and not least in general risk theory including applications thereof.
Speaker: Taiho Wang (CUNY, Baruch College)
Title: Executions in competition under Erlang kernel
Abstract:
We consider the problem of multiple order executions in competition as differential games and investigate their associated equilibria in two regimes: Stackelberg and Nash games. Price impact during execution comprises of the components of permanent, transient with delay kernel of Erlang type, and temporary or slippage impacts. The Erlang type kernel provides the flexibility of specifying a maximal impact from the lagged past tradings as opposed to sheer decaying kernels such as exponential or power law. The resulting price impact model remains Markovian in an extended, but finite dimensional, state space. Dynamic programming principle is thus applicable and equilibria in the two differential games are obtained subject to solving systems of Riccati equations. Numerical experiments are conducted for illustration of the theoretical results. The talk is based on a joint work with Michele Aleandri and Marina Di Giacinto.
Speaker 1: Ryoji Takano (Osaka University), 16:30--17:30
Title 1: Large deviation principle for rough volatility models
Abstract 1: A rough volatility model is a stochastic volatility model for an asset price process with volatility being rough, meaning that the H\”{o}lder regularity of the volatility path is less than half. In this talk, we will focus on the asymptotic behavior of the implied volatility for the short maturity and show that the short-time large deviation principle for rough volatility models characterize the asymptotic behavior of the implied volatility.
Speaker 2: Yushi Hamaguchi (Kyoto University), 17:45–18:45
Title 2: A generalized coupling approach for the weak approximation of stochastic functional differential equations (Abstract)
Abstract 2: In this talk, we study functional type weak approximation of weak solutions of stochastic functional differential equations by means of the Euler--Maruyama scheme. Under mild assumptions on the coefficients, we provide a quantitative error estimate for the weak approximation in terms of the Lévy--Prokhorov metric of probability laws on the path space. The weak error estimate obtained in this paper is sharp in the topological and quantitative senses in some special cases. We apply our main result to ten concrete examples appearing in a wide range of science and obtain a weak error estimate for each model. The proof of the main result is based on the so-called generalized coupling of probability measures. This talk is based on a joint work with Dai Taguchi (Kansai University). The preprint is available at arXiv:2412.18523.
Speaker : Ritsusamuel Otsubo (Industrial Research Center of Shiga Prefecture)
Title : Study on Control for Hypothesis Testing of Dynamic Systems
Abstract : Currently, industrial product testing faces challenges such as a shortage of personnel and significant mental and physical burdens. As a result, automation has become an urgent necessity to address these issues. When testing components such as motors and hydraulic pistons, a method is employed where input is applied to the product, and its output is analyzed to determine whether it functions normally or abnormally. In such tests, it is crucial to develop a control system that can efficiently obtain the required information while minimizing the strain on both the test object and the equipment. Additionally, the system must maintain robustness against disturbances and noise to ensure reliable results. In this seminar, we address hypothesis testing problems for parameters that characterize one-dimensional dynamic linear systems. The random disturbance of these systems is modeled as a stochastic variable defined on a space of continuous functions, characterized by its power spectral density. We also examine the behavior of linear systems under the influence of random disturbance. Additionally, we discuss an approximation of the random disturbance using the Ornstein-Uhlenbeck process. Based on these discussions, we consider the design of control systems to address these challenges. (The talk will be given in Japanese)