April 18, 2024. Probability and Mathematical Finance Seminar & Discussion.

Seminar: 16:30--18:30, Discussion: 18:30--22:30  (with some meals offered)

       Speaker 1: Jie Yen Fan (Monash University)

       Speaker 2: Ju-YI Yen (University of Cincinnati)

       Title 1: Mimicking: Martingales with Matching Marginals (Lecture 2)

       Title 2: A brief discussion on Brownian motion and related processes with applications (Lecture 2)

       Note: Dinner will be served to participants as the discussion part covers the dinner time.

Abstracts:  

June 13, 2024. Probability and Mathematical Finance Seminar & Discussion.

Seminar: 16:30--17:30, Discussion: 17:30--22:30  (with some meals offered)

       Speaker: 田中章博（三井住友銀行）

       Title: Weak approximation for a Black-Scholes type regime switching model

       Note: Dinner will be served to participants as the discussion part covers the dinner time.

Abstract:  レジームスイッチ型のブラックショールズモデルに対するヨーロピアンタイプのオプションのモンテ

カルロシミュレーション方法を提案する. プロセスが分割区間の境界点から離れる場合にはオイラース

キームを、プロセスが分割区間の境界点付近にある場合にはスキューブラウン運動を組み合わせた近似方法を提案し、弱近似誤差が指数関数的に小さくなることを示し、いくつかのシミュレーション結果を示す。

June 27, 2024. Probability and Mathematical Finance Seminar & Discussion. 

Seminar: 16:30--18:30, Discussion: 18:30--22:30  (with some meals offered)

Speaker 1: Anna Aksamit（Usydney), 16:30-17:30

Speaker 2: Hoang Vu (UC Santa Barbara), 17:30-18:30

Title 1: Introduction to robust finance I

Title 2: Heterogenous Macro-Finance Model: A Mean-field Game Approach

Abstract 1: 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.

Abstract 2: We investigate the capital allocation and wealth distribution of heterogeneous agents in the

economy during booms and busts using tools from mean-field games. Two groups in our

models, namely the expert and the household, are interconnected within and between their

classes through the law of capital processes and are bound by financial constraints. Such

mean-field interaction explains why experts accumulate lots of capital in the good times and

reverse their behavior quickly in the bad times even in the absence of aggregate macro shocks.

When the common noises from the market get involved, the financial friction amplifies the

mean-field effect and leads to experts’ capital fire sales. Moreover, the implicit interlink

between and within heterogeneous groups demonstrates the slow economic recovery and

characterizes the deviating and FOMO behaviors of the households in comparison to their

counterparts. Our model also gives a fairly explicit representation of the equilibrium solution

without exploiting complicated numerical approaches.

Keywords: Macro-Finance Model, Mean-field Games, Heterogeneity, Financial Friction

July 25, 2024. Probability and Mathematical Finance Seminar & Discussion. 

Seminar: 15:30--18:30, Discussion: 18:30--22:30  (with some meals offered)

Speaker 1: Daiki Tagami (Oxford University), 15:30-17:00

Speaker 2: Hau-Tieng Wu (NYU Courant Institute of Mathematical Sciences), 17:00-18:30

Title 1: tstrait: a quantitative trait simulator for ancestral recombination graphs

Title 2: Statistical Inference for Nonstationary Time Series via Phase-Driven Time-Frequency Analysis 

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.

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.