Seminars

2019

Date Information
​20 November 2019 Title: ​Bernstein-Bezier Polynomials for High Order Finite Element Approximation

Speaker: Professor Mark Ainsworth
Time: 10.30am – 11.30am

Abstract: ​​
We explore the use of Bernstein polynomials as a basis for finite element approximation on simplices in any spatial dimension. The Bernstein polynomials have a number of interesting properties that have led to their being the industry standard for visualisation and CAGD. It is shown that the basis enables the element matrices for the standard finite element space, consisting of continuous piecewise polynomials of degree n on simplicial elements in Rd, to be computed in optimal complexity O(p^2d). The algorithms take into account numerical quadrature; are applicable to nonlinear problems; and do not rely on precomputed arrays containing values of one-dimensional basis functions at quadrature points (although these can be used if desired). The standard tools for the evaluation of Bezier curves and surfaces is the de Casteljau algorithm. The archetypal pyramid algorithm is the de Casteljau algorithm. Pyramid algorithms replace an operation on a single high order polynomial by a recursive sequence of self-similar affine combinations and, as such, offer significant advantages for high order finite element approximation. We develop and analyze pyramid algorithms for the efficient handling of all of the basic finite element building blocks, including the assembly of the element load vectors and element stiffness matrices. The complexity of the algorithm for generating the element stiffness matrix is optimal. A new, nonuniform order, variant of the de Casteljau algorithm is developed that is applicable to the variable polynomial order case but incurs no additional complexity compared with the original algorithm. The work provides the methodology that enables the efficient use of a completely general distribution of polynomial degrees without any restriction in changes between adjacent cells, in any number of spatial dimensions.

Host: Associate Professor Wang Li-Lian
​11 November 2019 ​​​NUS meets NTU Mini-workshop in Mathematical Finance 

Title: Portfolio diversification and model uncertainty: a robust dynamic mean-variance approach

Speaker: Assistant Professor Chao Zhou
Time: 2.00pm – 2.45pm

Abstract

This talk is concerned with multi-asset mean-variance portfolio selection problem under model uncertainty. We develop a continuous time framework for taking into account ambiguity aversion about both expected rate of return and correlation matrix of stocks, and for studying the effects on portfolio diversification.  

We prove a separation principle for the associated robust control problem formulated as a mean-field type differential game, which allows to reduce the determination of the optimal dynamic strategy to the parametric computation of the minimal risk premium function. 

Our results provide a justification for under-diversification, as documented in empirical studies, and that we explicitly quantify in terms of correlation and Sharpe ratio ambiguity parameters.  In particular, we show that an investor with a poor confidence in the expected return estimation does not hold any risky asset, and on the other hand, trades only one risky asset when the level of ambiguity on correlation matrix is large. This extends to the continuous-time setting the results obtained by Garlappi, Uppal and Wang (2007), and Liu and Zeng (2017) in a one-period model. 

Based on joint work with Huyên Pham (Paris Diderot University) and Xiaoli Wei (University of California, Berkeley).

Title: Systemic Portfolio Diversification
Speaker: Professor Marko Weber
Time: 2.55pm –3.40pm

Abstract

We study the implications of fire-sale externalities on balance sheet composition. Banks choose their asset holdings accounting for the liquidation costs incurred when they sell assets to manage their leverage. Our analysis highlights the fundamental trade-off between diversification at the bank and at the systemic level. While sacrificing diversification benefits to reduce portfolio commonality may increase the bank's idiosyncratic probability of liquidation, it also lowers the endogenous probability of a costly widespread sell-off. We show that higher heterogeneity in banks' leverage is socially beneficial because it gives banks stronger incentives in achieving systemic diversification. The socially optimal level of systemic diversification can be attained by taxing banks for creating interlinked balance sheets with high concentration on illiquid assets.

Title: Mean Field Leader-Follower Games with Terminal State Constraint
Speaker: Research Fellow Dr FU Guanxing
Tme: 4.00pm –4.30pm

Abstract

We analyze linear McKean-Vlasov forward-backward SDEs arising in leader-follower      games with mean-field type control and terminal state constraints on the state process. We establish an existence and uniqueness of solutions result for such systems in time-weighted spaces as well as a convergence result of the solutions with respect to certain perturbations of the drivers of both the forward and the backward component. The general results are used to solve a novel single-player model of portfolio liquidation under market impact with expectations feedback as well as a novel Stackelberg game of optimal portfolio liquidation with asymmetrically informed players.

Title: Deep Learning Algorithm to solve Portfolio management with Proportional Transaction Cost
Speaker: PhD Student Zhang Weiwei
Time: 4.30pm –5.00pm

Abstract

We propose a deep learning based numerical scheme to solve transaction cost problems, compare its effectiveness with a penalty partial differential equation (PDE) method, and further extend it to multi-asset cases which existing numerical methods can not be applied to due to the curse of dimensionality. Deep learning algorithm directly approximates the optimal trading strategies by a feedforward neural network at each discrete time. It is observed that deep learning approach can achieve satisfying performance to characterize optimal buy and sell boundaries and thus value function.

Host: Nanyang Assistant Professor Ariel Neufeld 

Division of Mathematical Sciences, School of Physical and Mathematical Sciences ​

​​31 October 2019​ ​​Title: Stability of (F-)BSDEs under Mémin's framework​

Postdoctoral Assistant Professor Alexandros Saplaouras
Time: ​5.00pm – 6.00pm

Abstract: Backward Stochastic Differential Equations, in short BSDE, have become a particularly active field of research, due to their numerous potential applications to mathematical finance, partial differential equations, game theory, economics, and more generally in stochastic calculus and analysis. In this talk we will discuss initially the stability property of special semimartingales, where we refine the result obtained by Mémin (2003). Then we focus on the special case where the sequence of semimartingales consists of solutions of Backward Stochastic Differential Equations with Jumps, in short BSDEJ, and we provide a suitable framework for obtaining the stability property of BSDEJ. Afterwards, we will proceed on some ongoing research and present some ideas on the stability property of Forward-Backward Stochastic Differential Equations with Jumps (FBSDEJ).

Host: Nanyang Assistant Professor Ariel Neufeld 
Division of Mathematical Sciences, School of Physical and Mathematical Sciences ​
​31 October 2019 ​​Title: Improved Fréchet-Hoeffding bounds, optimal transport and model-free finance​

Assistant Professor Antonis Papapantoleon
Time: 04.00pm – 5.00pm​

Abstract:
This talk considers model-free bounds for multi-asset option prices in a setting where the marginals are known and the dependence structure is partially known. We will first present methods to sharpen the classical Fréchet-Hoeffding bounds on copulas using additional information on the dependence structure, and discuss their application in option pricing, portfolio Value-at-Risk and the detection of arbitrage. Then, we will consider model-free hedging of multi-asset option prices in the presence of additional information on the dependence structure. An extension of the classical optimal transport superhedging duality will allow us to provide new insights in model-free hedging, and show (non) sharpness of the improved Fréchet-Hoeffding bounds.

Host: Nanyang Assistant Professor Ariel Neufeld 
Division of Mathematical Sciences, School of Physical and Mathematical Sciences 
​4 October 2019 ​Title: On the Artificial Boundary Conditions and PML Methods for Schrödinger Equations

Professor Xavier Antoine
Time: 3.00pm – 4.00pm

Abstract:
In this talk, I will introduce some mathematical methods to build artificial boundary conditions for Schrödinger equations. The derivation of stable discretization schemes will also be developed. In addition, I will provide shortly some recent results on the implementation of the Perfectly Matched Layer for the Schrödinger equation approximated by pseudospectral methods. 

Host: Associate Professor Wang Li-Lian
Division of Mathematical Sciences, School of Physical and Mathematical Sciences
​27 September 2019​ FinTech Seminar Series

Title: ASEAN FinTech Landscape & Women In FinTech

Neha Mehta (Founder of FemTech Partners)

Time: 10:30 AM - 12:30 PM
Venue: SPMS LT2, SPMS 03-03

Abstract:

Is Singapore the best FinTech Hub? Is 50% female representation in FinTech a far fetched dream? This workshop will answer some of these burning questions and broadly cover ASEAN FinTech landscape and Women in FinTech.

ASEAN FinTech landscape will give a bird's eye-view on every jurisdiction within ASEAN- key FinTech markets, the soft/light regulation, regulators managing the thin line between promoting FinTech Innovation and market protection. It will give participants an understanding of the regulatory sandbox, Initial Coin Offerings (ICO), Future Trends of FinTech, Blockchain, RegTech, InsurTech and AI. The workshop will also focus on API’s, Open Banking and throw some light on project Ubin of the Monetary Authority Bank of Singapore (MAS) - clearing and settlement of payments and securities using Blockchain. LASTLY, makes sense of the buzz around Data Privacy and General Data Protection Regulation (GDPR).

The other part of the workshop will focus on "Women in FinTech"; only 2% of Venture Capital funding goes to women entrepreneurs. Women need to step UP and break into the old boys club to shine in this domain. Learn the art of selling yourself and be market ready for a great career in the FinTech industry. The much needed "soft" and "hard" skills to launch yourself into the ever evolving world of FinTech will be the focus of this session.

Host: Asst Prof Pun Chi Seng (Director of MSc in FinTech)​
Division of Mathematical Sciences, School of Physical and Mathematical Sciences​

​26 September 2019​ Title: Computation of Free Energy at ab initio QM/MM Level Made Orders of Magnitude Faster via the Reference-Potential Approach

Professsor Ye Mei
Time: 02.00pm – 3.30pm

Abstract:

​Multiscale simulation methods are now playing a more and more important role for the study of complex chemical systems. However, application of these methods is often limited by its computational expense, especially when ab initio quantum mechanical methods are inevitable for the description of the processes, for instance chemical reactions. Reference-potential methods can be a cure for this difficulty, in which the phase-space sampling and ensemble average calculations are separated using different Hamiltonians. In the latter, the weight for each sample should be properly considered, if a non-Boltzmann statistical ensemble is used. In this lecture, I will introduce the development of reference-potential methods for the calculations of differences in state free energies and free energy profiles for specific chemical processes with samples extracted from single and mixed ensembles.

Host: Assistant Professor Kelin Xia
Division of Mathematical Sciences, School of Physical and Mathematical Sciences​
​18 September 2019  ​Title: Bayes-optimal filtering in the tensor-train format

Professor​ Colin Fox
Time: 04.00pm – 5.00pm

Abstract:
Optimal sequential Bayesian inference, or filtering, for the state of a dynamical system requires solving a partial differential equation. For low-dimensional, smooth systems the finite-volume method is an effective solver that converges to the optimal continuous-time solution and estimates. For higher-dimensional systems the curse of dimensionality may be overcome by representing density functions by an interpolated tensor train decomposition. 
We give examples of filtering for continuous-time and discrete-time systems to demonstrate that the resulting Bayes-optimal filter is able to handle non-linear systems and multi-modal filtering distributions.​

​Host: Associate Professor Hoang Viet Ha
Division of Mathematical Sciences, School of Physical and Mathematical Sciences​

​​13 September 2019 ​​Title: P1–nonconforming polyhedral finite elements in high dimensions

Professor Dongwoo Sheen
Time: 11.00am – 12.00pm

Abstract:
We consider the lowest–degree nonconforming finite element methods for the approximation of elliptic problems in high dimensions. The P1–nonconforming polyhedral finite element is introduced for any high dimension. Our finite element is simple and cheap as it is based on the triangulation of domains into polytopes, which are combinatorially equivalent to the d–dimensional unit cube, rather than the triangulation of domains into simplices. Our nonconforming element is nonparametric, and on each polytope it contains only linear polynomials, but it is sufficient to give optimal order convergence for second–order elliptic problems.​

​Host: Associate Professor Hoang Viet Ha
Division of Mathematical Sciences, School of Physical and Mathematical Sciences​
​15 August 2019 ​​Title: Tight Bounds for L1 Oblivious Subspace Embeddings

Associate Professor David Woodruff
Time: 3.00pm to 4.00pm

Abstract

Oblivious subspace embeddings have proven to be an essential ingredient for approximately solving numerical linear algebra problems, such as regression and low-rank approximation. 
While for p = 2 there are nearly optimal tradeoffs in terms of the dimension, distortion, and sparsity, for the important case of p = 1, much less was known. In this talk I will present our results on l1 oblivious subspace embeddings, including (i) nearly optimal lower bounds and (ii) new constructions for sparse l1 oblivious subspace embeddings. 
Oblivious subspace embeddings are crucial for distributed and streaming environments, as well as entrywise lp low rank approximation. Our results give improved algorithms for these applications.
Based on joint work with Ruosong Wang. ​

Host: Dr Li Yi, Division of Mathematical Sciences
School of Physical and Mathematical Sciences​
​2 August 2019 ​Title: Self-Dual Codes over Finite Fields​

Dr. Lin SOK
Time: 11.00am – 12.00pm

Abstract

In this talk, we study self-dual codes over finite fields using tools from algebraic function field of one variable. An algebraic geometry code is defined with two divisors G and D, where D is the sum of n points on a specified algebraic curve. We characterize self-orthogonality of the 0-genus code in terms of the divisors G and D and the value of a well-chosen derivative polynomial at points P_i for i from 1 to n. We explore the existence problem of MDS self-dual codes in odd characteristic cases and explicitly construct families of new MDS self-dual codes.​

​Host: Professor Ling San
Division of Mathematical Sciences, School of Physical and Mathematical Sciences​
​31 July 2019

​Title: Seismic tomography, frozen Gaussian approximation and deep learning

Associate Professor Xu Yang
Time: 2:00pm – 2:30pm

Abstract

Three-dimensional (3-D) elastic wave propagation and seismic tomography is computationally challenging in large scales and high-frequency regime. In this talk, we propose the frozen Gaussian approximation (FGA) to compute the 3-D elastic wave propagation and use it as the forward modeling tool for seismic tomography with high-frequency data. The accuracy and parallelizability of the FGA algorithm is illustrated by comparing to the spectral element method. With a parallel FGA solver built as a computational platform, we explore various applications in 3-D seismic tomography, including seismic travel time tomography and full waveform inversion, respectively. Global minimization for seismic tomography is investigated based on particle swarm algorithm. We also apply the FGA algorithm to train deep neural networks to learn the object of low velocity in the interested areas.​

Host: Assistant Professor Tong Ping
Division of Mathematical Sciences, School of Physical and Mathematical Sciences​​
​22 July 2019 ​Title: CVA Wrong Way Risk: Calibration using a Quanto CDS Basis

Dr. CHUNG Tsz-Kin (Bill)
Time: 3.00pm – 4.00pm

Abstract

In this article, we discuss the calibration of wrong way risk (WWR) model by using information from the credit default swap (CDS) market. A quanto CDS provides credit protection against the default of a reference entity but is denominated in a non-domestic currency. The payoff of a quanto CDS contract, therefore, reflects the market-implied interaction of FX risk and a credit event. This in turn, defines the cost of hedging WWR for an FX-sensitive portfolio. Our empirical evidence shows that the implied FX jump sizes are significant for a wide range of corporates. For systemic counterparties, the CVA WWR add-on could be 40% higher than the standard case, and choosing a proper jump-at-default WWR model is critical to capture the impact. In contrast, historical correlation gives the incorrect relationship (right-way risk) and cannot calibrate to the market prices in many cases, leading to the mispricing of CVA WWR.

Joint work with Jon Gregory​

Host: Assistant Professor Pun Chi Seng Patrick
Division of Mathematical Sciences, School of Physical and Mathematical Sciences​
​21 May 2019​ ​​Title: Algorithms for Wave Scattering of Random Media: Fast multipole method in layered media and a phase shift deep neural network for wideband learning

Professor ​Wei Cai​
Time: ​3.00pm – 4.00pm

Abstract​

In this talk, we will present two algorithms and numerical results for solving electromagnetic wave scattering of random meta-materials.  Firstly, a fast multipole method for 3-D Helmholtz equation for layered media will be presented based on new multipole expansion (ME) and multipole to local translation (M2L) operators for layered media Green's functions. Secondly, a  parallel phase shift deep neural network (PhaseDNN) is proposed for wideband data learning. In order to achieve uniform convergence for low to high frequency content of data,  phase shifts are used to convert high frequency learning to low frequency learning. Due to the fast learning of many DNNs in the low frequency range, PhaseDNN is able to learn wideband data uniformly in all frequencies.

Host: Associate Professor Wang Li-Lian
Division of Mathematical Sciences, School of Physical and Mathematical Sciences
​21 May 2019 ​Title: Approximation Theory and Regularization for Deep Learning

Assistant Professor Haizhao Yang
Time: 4.00pm – 5.00pm

Abstract​

This talk introduces new approximation theories for deep learning in parallel computing and high dimensional problems. We will explain the power of function composition in deep neural networks and characterize the approximation capacity of shallow and deep neural networks for various functions on a high-dimensional compact domain. Combining parallel computing, our analysis leads to an important point of view, which was not paid attention to in the literature of approximation theory, for choosing network architectures, especially for large-scale deep learning training in parallel computing: deep is good but too deep might be less attractive. Our analysis also inspires a new regularization method that achieves state-of-the-art performance in most kinds of network architectures

Host: Associate Professor Wang Li-Lian
Division of Mathematical Sciences, School of Physical and Mathematical Sciences
​15 May 2019  ​Title: A general approach to non-Markovian time-inconsistent stochastic control for sophisticated players​

 Assistant Professor​ Dylan Possamai​
Time: 4.00pm – 5.00pm

Abstract

This paper is the first attempt at a general non-Markovian theory of time-inconsistent stochastic control problems in continuous-time. We consider sophisticated agents who are aware of their time-inconsistency and take into account in future decisions. We prove here that equilibria in such a problem can be chara​cterised through a new type of multi-dimensional system of backward SDEs, for which we obtain wellposedness. Unlike the existing literature, we can treat the case of non-Markovian dynamics, and our results go beyond verification type theorems, in the sense that we prove that any (strict) equilibrium must necessarily arise from our system of BSDEs. This is a joint work with Camilo Hernández, Columbia University.

Host: Nanyang Assistant Professor Ariel Neufeld 
Division of Mathematical Sciences, School of Physical and Mathematical Sciences 
​29 April 2019 ​Title: Finite element methods with discontinuous approximations

Professor Xiu Ye​
Time: 10.30am – 11.30am

Abstract​

In this presentation, different finite element methods with discontinuous approximations will be discussed including IPDG, HDG and specially WG finite element methods as well as the relations between them. In addition, a new conforming DG finite element method will be introduced which combines the features of both conforming finite element method and discontinuous Galerkin method.

Host: Assistant Professor Kelin Xia
Division of Mathematical Sciences, School of Physical and Mathematical Sciences

​4 April 2019 Title:  Fair Allocation of Combinations of Indivisible Goods and Chores

Ayumi Igarashi
Time:  3.30pm – 4.30pm

Abstract

We consider the problem of fairly dividing a set of items. Much of the fair division literature assumes that the items are “goods” i.e., they yield positive utility for the agents. There is also some work where the items are “chores” that yield negative utility for the agents. In this work, we consider more general scenarios where for any item, an agent may have negative or positive utility for it. We show that whereas some of the positive axiomatic and computational results extend to this more general setting, others do not. We present several new algorithms for finding fair allocations in the general setting. We also point out several gaps in the literature regarding the existence of allocations satisfying certain fairness and efficiency properties and further study the complexity of computing such allocations. This is a joint work with Haris Aziz, Ioannis Caragiannis, and Toby Walsh.

​​​​​​Host: Nanyang Assistant Professor Bei Xiaohui
Division of Mathematical Sciences, School of Physical and Mathematical Sciences
4 April 2019  Title:  An Ordinal Minimax Theorem

Warut Suksompong
Time: 2.30pm – 3.30pm

Abstract

In the early 1950s Lloyd Shapley proposed an ordinal and set-valued solution concept for zero-sum games called weak saddle. We show that all weak saddles of a given zero-sum game are interchangeable and equivalent. As a consequence, every such game possesses a unique set-based value. Our result can be seen as an ordinal version of the celebrated minimax theorem of John von Neumann. No prior knowledge of game theory or economics is required---I will explain all the necessary concepts in the talk.

Host: Nanyang Assistant Professor Bei Xiaohui
Division of Mathematical Sciences, School of Physical and Mathematical Sciences 
21 March 2019 Title: FBSDEs with discontinuous coefficients

Assistant Professor Ludovic Tangpi
Time: 4.00pm – 5.00pm 

Abstract

In this talk we consider well-posedness of systems of forward and backward stochastic differential equations when (at least some of) the coefficients are merely assumed to be measurable. Since such systems cannot be tackled with classical fixed point theory, we device new methods based on "domination arguments" and Malliavin calculus techniques.

The talk is based on joint works with K. Bahlali and O. Menoukeu-Pamen

Host: Nanyang Assistant Professor Ariel Neufeld
Division of Mathematical Sciences, School of Physical and Mathematical Sciences
12 February 2019  Title: Virtual element methods for elliptic variational inequalities of the second kind

Professor Huang Jianguo
Time: 4.00pm – 5.00pm

Abstract

In this talk, we are concerned with virtual element methods for solving elliptic variational inequalities (EVIs) of the second kind. First, a general framework is provided for the numerical solution of the EVIs and for its error analysis.  Then, two virtual element methods are applied to solve two representative EVIs: a simplified friction problem and a frictional contact problem, respectively. Optimal order error estimates are derived for the virtual element solutions of the two EVIs, including the effects of numerical integration for the non-smooth term in the EVIs.  A fast solver is introduced to solve the discrete problems. Several numerical examples are included to show the numerical performance of the proposed methods. This is a joint with Fang Feng from Shanghai Jiao Tong University and Weimin Han from University of Iowa.

Host:  Assistant Professor Tong Ping
Division of Mathematical Sciences, School of Physical and Mathematical Sciences
30 January 2019 Title: Analytical Nonlinear Shrinkage of Large-Dimensional Covariance Matrices  

Professor Michael Wolf 
Time: 3.30pm – 4.30pm

Abstract

We have proposed an analytical method for nonlinear shrinkage of covariance matrices based on kernel estimation in large dimensions. It enjoys the following merits:

1) Performs as well as existing methods

2) Easy to implement

3) Computationally cheap

4) More potential to accommodate future variations and extensions


Host: Associate Professor Pan Guangming
Division of Mathematical Sciences, School of Physical and Mathematical Sciences
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