• Speaker 2:Yushi Hamaguchi (Kyoto University) 17:45 –18:45
• Title: A generalized coupling approach for the weak approximation of stochastic functional differential equations
• Abstract:

日時: 2025年1月9日 (木) 18:00–19:30

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

講演者: Taiho Wang (CUNY Baruch College) 

講演題目: Executions in competition under Erlang kernel

講演要旨: 

Title: Markov Chain Monte Carlo: how and why?Ⅲ

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.

Title: Markov Chain Monte Carlo: how and why? II

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 2: Andrea Macrina (University College London), 17:40–18:40

Title: Continuous-Time Quantile Processes with Applications in Finance and Insurance

Abstract: 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.