Speaker: Dr. Yimei Li from St. Jude Children’s Research Hospital

Date and Time: Friday, April 30, 2021, 11am – 12pm via Zoom. Please contact Qingning Zhou to obtain the Zoom link.

Title: Group sequential design for historical control trials using error spending functions

Abstract: Randomized clinical trials (RCTs) are considered the gold standard for clinical trials comparing treatment groups. However, historical control trials (HCTs) are an alternative to RCTs if randomization is not feasible because of ethical concerns, patient preference, limited patient populations, or regulatory acceptability. The major benefit of HCTs is that all patients can receive the new treatment with historical data providing the information for the control arm. Therefore, HCTs are useful for studies with limited patient populations. Group sequential designs using Lan-DeMets error spending functions are proposed for historical control trials with time-to-event endpoints. Both O’Brien–Fleming and Gamma family types of sequential decision boundaries are derived based on sequential log-rank tests, which follow a Brownian motion in a transformed information time. Simulation results show that the proposed group sequential designs using historical controls preserve the overall type I error and power. An example is provided to show how to use the method to design a Children Oncology Group High Grade Glioma trial.

Speaker: Dr. Andreas Artemiou from Cardiff University

Date and Time: Friday, April 16, 2021, 11am – 12pm via Zoom. Please contact Qingning Zhou to obtain the Zoom link.

Title: SVM-based real time sufficient dimension reduction

Abstract: We discuss in this talk one of the first efforts for real-time sufficient dimension reduction. Support Vector Machine (SVM) based sufficient dimension reduction algorithms were proposed the last decade to provide a unified framework for linear and nonlinear sufficient dimension reduction. We present our idea of using a variant of the classic SVM algorithm known as Least Squares SVM (LSSVM) to achieve real time sufficient dimension reduction. We demonstrate the computational advantages as well as the computational efficiency of our algorithm through simulated and real data experiments. This is joint work with my collaborators Yuexiao Dong (Temple University) and Seung Jun Shin (Korea University).

Speaker: Dr. Runhuan Feng from the University of Illinois at Urbana-Champaign

Date and Time: Friday, April 9, 2021, 12pm – 1pm via Zoom. Please contact Qingning Zhou to obtain the Zoom link.

Title: Modeling Financial Market Movement with Winning Streaks: Sticky Maximum Process

Abstract: Winning streaks appear frequently in all financial markets including equity, commodity, foreign exchange, real estate, etc. Most stochastic process models for financial market data in the current literature focus on stylized facts such as fat-tailedness relative to normality, volatility clustering, mean reversion. However, none of existing financial models captures the pervasive feature of persistent extremes: financial indices frequently report record highs or lows in concentrated periods of time. In this paper, we apply the technique of time change with local time to capture the market anomaly of persistent extremes. The new model which is driven by a sticky processes with moving boundaries { running maxima enables us to measure and assess the impact of persistent extremes on financial derivatives. Despite the time change construction, option prices are still solvable analytically. In addition, the model in this paper reveals a paradox that investors who bet on the growth of financial market may be worse off with pervasive winning streaks in the market.

Speaker: Dr. Yanzhi Zhang from Missouri University of Science and Technology

Date and Time: Friday, April 2, 2021, 11am – 12pm via Zoom. Please contact Qingning Zhou to obtain the Zoom link.

Title: Numerical Methods for Nonlocal Problems with the Fractional Laplacian

Abstract: Recently, the fractional Laplacian has received great attention in modeling complex phenomena that involve long-range interactions. However, its nonlocality introduces considerable challenges in both mathematical analysis and numerical simulations. So far, numerical methods for the fractional Laplacian still remain limited. It is well known that the fractional Laplacian can be defined either in a pseudo-differential form via the Fourier transforms or in a hypersingular integral form. In this talk, I will discuss three different groups of numerical methods to discretize the fractional Laplacian. In the first group, we introduce the Fourier pseudospcetral methods based on the pseudo-differential form of the fractional Laplacian. The second group is operator factorization methods based on the hypersingular integral definition.  In the third group, we combine both pseudo-differential and hypersingular integral forms of the fractional Laplacian and introduce meshfree methods with radial basis functions. The properties of these methods will be discussed, and some applications of nonlocal problems with the fractional Laplacian will also be demonstrated.

Speaker: Dr. Nam Le from Indiana University Bloomington

Date and Time: Wednesday, March 24, 2021, 10am – 11am via Zoom. Please contact Qingning Zhou to obtain the Zoom link.

Title: Liouville type theorems for the Monge-Ampere equation

Abstract: Liouville type theorems in Partial Differential Equations are concerned with classification of global solutions. The Monge-Ampere equation consists of prescribing the determinant of the Hessian of a convex function. In this talk, we will review some Liouville type theorems for the Monge-Ampere equation in the whole space, on the half space, and we will discuss in depth the case in the first quadrant in the plane. Application will be given to global second order derivative estimates for the non-degenerate Monge-Ampere equation in convex polygonal domains in the plane. This talk is based on joint work with Ovidiu Savin. The talk will be accessible to general mathematical audience.

Speaker: Dr. Xiaochuan Tian from the University of California, San Diego

Date and Time: Thursday, December 10, 2020, 12pm – 1pm via Zoom. Please contact Qingning Zhou to obtain the Zoom link.

Title: Reproducing kernel collocation methods for nonlocal models: asymptotic compatibility and numerical stability

Abstract: Nonlocal continuum models are in general integro-differential equations in place of the conventional partial differential equations. While nonlocal models show their effectiveness in modeling a number of anomalous and singular processes in physics and material sciences, for example, the peridynamics model of fracture mechanics, they also come with increased difficulty in computation with nonlocality involved. Aiming at both rigorous numerical analysis and computational efficiency, we present the reproducing kernel collocation methods, a class of meshfree methods, for approximating nonlocal models characterized by a length parameter that may change with the models. A central idea is to design asymptotic compatible schemes that are robust under the change of the nonlocal length parameter.

Speaker: Dr. Kin Yau Wong from the Hong Kong Polytechnic University

Date and time: Friday, November 20, 2020, 10am – 11am via Zoom. Please contact Qingning Zhou to obtain the Zoom link.

Title: Score Tests with Incomplete Covariates and High-Dimensional Auxiliary Variables

Abstract: Analysis of modern biomedical data is often complicated by the presence of missing values. To improve statistical efficiency, it is desirable to make use of potentially high-dimensional observed variables to impute or predict the missing values. Although many methods have been developed for prediction using high-dimensional variables, it is challenging to perform valid inference based on the predicted values. In this presentation, we develop an association test for an outcome variable and a potentially missing covariate, where the covariate can be predicted using selected variables from a set of high-dimensional auxiliary variables. We establish the validity of the test under general model selection procedures. We demonstrate the validity of the proposed method and its advantages over existing methods through extensive simulation studies and provide an application to a major cancer genomics study.

Speaker: Dr. Jennifer Alonso Garcia from Université Libre de Bruxelles

Date and time: Friday, November 13, 2020, 11am – 12pm via Zoom. Please contact Qingning Zhou to obtain the Zoom link.

Title: Taxation and Policyholder Behavior: The Case of Guaranteed Minimum Accumulation Benefits

Abstract: This paper considers variable annuity contracts embedded with guaranteed minimum accumulation benefit (GMAB) riders when policyholder’s proceeds are taxed. These contracts promise the return of the premium paid by the policyholder, or a higher stepped up value, at the end of the investment period. A partial differential valuation framework, which exploits the numerical method of lines, is used to determine fair fees that render the policyholder and insurer profits neutral. Two taxation regimes are considered; one where capital gains are allowed to offset losses and a second where gains do not offset losses, reflecting stylized institutional arrangements in Australia and the US respectively. Most insurance providers highlight the tax-deferred feature of a variable annuity. We show that the regime under which the insurance provider is taxed significantly impacts supply and demand prices. If losses are allowed to offset gains then this enhances the market, narrowing the gap between fees, and even producing higher demand than supply fees. On the other hand, when losses are not allowed to offset gains, then the demand-supply gap increases. When charging the demand price, we show that insurance companies would be profitable on average. Low (high) Sharpe ratios are not as profitable as policyholders are more likely to stay long (surrender).

Speaker: Dr. Linquan Bai (Department of Systems Engineering & Engineering Management, UNC Charlotte)

Date/Time/Place: 2:00–3:00pm, March 27 (Friday), Fretwell 315.

Title: Transition to Risk Driven Power Grid Operation and Management

Abstract: Affordable and reliable electricity is fundamental to society. Today’s power grid is facing more risks than ever from uncertain renewable power generation, more frequent severe weather events, and cyber-attacks. Integrating emerging technologies such as renewable energy, energy storage, and electric vehicles, the management system of the power grid should evolve to a risk-driven paradigm to effectively manage, hedge and mitigate the system risks. The transition of the power grid management system necessitate advanced risk-theory to analyze probability and uncertainty quantification of renewable generation and vulnerability in power grid topology, optimization approaches for risk-averse optimal power grid scheduling, machine learning for cyberattack detection, etc. I will present the challenges today’s power grid is facing and applications of these new theories and methodologies in addressing the challenges.

Conference room, 11:00 am-12:00 pm

Dr. Tien-Khai Nguyen, NC State University.

Title: Differential Game Models of Optimal Debt Management 
Abstract: In this talk, I will present recent results on game theoretical formulation of optimal debt management problems in infinite time horizon with exponential discount, modeled as a noncooperative interaction between a borrower and a pool of risk-neutral lenders. Here, the yearly income of the borrower is governed by a stochastic process and bankruptcy instantly occurs when the debt-to-income ratio reaches a threshold. Since the borrower may go bankrupt in finite time, the risk-neutral lenders will charge a higher interest rate in order to compensate for this possible loss of their investment. Thus, a “solution” must be understood as a Nash equilibrium, where the strategy implemented by the borrower represents the best reply to the strategy adopted by the lenders, and conversely. This leads to highly nonstandard optimization processes.