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. European Journal of Operational Research, 252 (2016), 676-686.
• Winston S. Buckley and Hongwei Long, A discontinuous mispricing model under asymmetric information. 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. Mathematical Finance Letters 2015:6 (2015), 1-12.
• Zdzislaw Brzezniak and Hongwei Long, A note on γ-radonifying and summing operators. 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. To appear in the Proceedings of the 60th 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