Dr. Hongwei Long

Education

• Ph.D. in    Mathematics, University of Warwick, England. 1998  

Research Interests

• Stochastic analysis
• Stochastic partial differential equations and their numerical solutions
• Nonlinear filtering theory and its applications
• Parameter estimation in nonlinear stochastic systems
• Mathematical finance

Research Description

Mathematical Finance - This is an interdisciplinary research area which has close connection and interaction with probability, statistics, engineering, optimization, control, and finance. The purpose is to use stochastic calculus, statistical inference, optimization and control to develop and analyze quantitative financial models and optimal investing strategies.

Parameter Estimation for Stochastic Systems - Many physical scenarios can be modeled by stochastic systems driven by noises with unknown parameters. The purpose of parameter estimation is to use statistical methods to derive an optimal and implementable estimator, and to study the consistency and asymptotics of the proposed estimator.

Filtering Theory and Its Applications - Filtering theory is an active and current research field with wide applications to real world problems arising in financial market, economic, communication networks, signal processing, target detection and tracking. The purpose of filtering is to find probabilistic knowledge of the past path, current state, or the future changes of the signal based on noisy observations.

Stochastic Partial Differential Equations - Stochastic partial differential equations can be used in many areas of science to model complex systems evolving over time. It is generally difficult to solve these equations analytically. It is desirable to develop numerical methods to approximate the solutions.

Stochastic Analysis - This is a research field with deep connection to classical probability, mathematical physics, ergodic theory, operator theory, and dynamical systems. It mainly focuses on the study of diffusions and the corresponding differential operators in infinite dimensional spaces by using methods from analysis and probability.

 Recent Publications

• Winston S. Buckley, Hongwei Long, and Mario Marshall, Numerical approximations of optimal portfolios in mispriced asymmetric Levy markets, (PDF file). European Journal of Operational Research, 252 (2016), 676-686.
• Winston S. Buckley and Hongwei Long, A discontinuous mispricing model under asymmetric information, (PDF file). European Journal of Operational Research, 243 (2015), 944-955.
• Winston Buckley, Hongwei Long, and Sandun Perera, The link between asymmetric and symmetric optimal portfolios in fads models, (PDF file). Mathematical Finance Letters 2015:6 (2015), 1-12.
• Zdzislaw Brzezniak and Hongwei Long, A note on γ-radonifying and summing operators, (PDF file). In Stochastic Analysis, Banach Center Publications, Volume 105, pp. 43-57, 2015.
• Hongwei Long, Chunhua Ma, and Yasutaka Shimizu, Least squares estimators for stochastic differentail equations driven by small Levy noise, (PDF file). To appear in the Proceedings of the 60^th ISI World Statistics Congress-ISI 2015.

Scholarly Activities

A.   Service at the Department /College Level

Served on various departmental committees: Research & Grant Committee, Math Day Committee, Undergraduate Committee, Graduate Committee, Evaluation Committee and Executive Committee. Served as Faculty Marshall for the Charles E. Schmidt College of Science at the FAU Commencement on August 4, 2009.

B.         Community Service

Volunteer as judge at the dispute center for several Mu Alpha Theta Math Competitions at FAU and local high schools; Volunteer for Florida Science Olympiad (FAU).

C.         Professional Service

Referee for

 Abstract and Applied Analysis

Acta Mathematica Scientia

Acta Mathematica Sinica

Communications in Statistics: Theory and Methods

Dynamics of Continuous, Discrete and Impulse Systems

Electronic Journal of Probability

Electronic Communication in Probability

Frontiers of Mathematics in China

IMA Journal of Management Mathematics

International Journal of Stochastic Analysis

Journal of Applied Mathematics and Stochastic Analysis

Journal of computational and Applied Mathematics

Journal of Econometrics

Mathematics and Computers in Simulation

SIAM Control and Optimization

Signal Processing Letters

Statistics and Probability Letters

 Personal Website

including a full list of publications: http://brain.math.fau.edu/Long/hlong.htm