Capital Market Research

• Quantitative risk management for mortgage pipeline.
• Developed cash flow models for reverse mortgage products.
• Created various mortgage rates forecasting models using time series analysis.
• Built mortgage prepayment models which use loan attribution to forecast the probability of prepayment for every month of a loan’s remaining term. Calibrated to millions of loan records and carried out forward prepayment speed test.
• Created and streamlined hedging strategies for mortgage backed securities using TBA, swap, swaption based on risk matrices of key rate durations, mortgage spread duration, Vega and convexity.

American Option Pricing Models

• Variational inequalities formulation for American options.
• Investigated sensitivity of the option price to the final payoff change.
• Designed accurate methods to determine the optimal exercise boundary.

Finite Element Models for Free Boundary Problems

• Developed fast algorithms for solving a class of free boundary problems called obstacle problems which arise from the filtration dam problem, the Stefan problem, and the American option pricing models.
• Derived a general condition for the convergence of free boundaries of discrete solutions to the free boundary of the continuous solution. The interface between wetted and unwetted regions in dam problem and early exercise boundary of American options are typical free boundaries.
• Established a monotonicity principle for a finite element approximation of obstacle problem. Obtained an optimal error estimate under maximum norm which improved two well-known results established by Nitsche and Baiocchi thirty years ago.
• Developed a numerical model for a Bingham fluid flow in a cylindrical pipe using a regularization method.

Stochastic Models and Monte Carlo Simulations

• Developed and implemented numerical algorithms for a stochastic multiphase fluid mixing model.
• Discovered an asymmetry effect ("North Pole Effect") on axisymmetric flow analyzed this effect on various statistics of the chaotic fluid mixing by carrying out Monte Carlo simulations.

Finite Difference Models for Multiphase Supersonic Flow and Shock Waves

• Developed front tracking algorithms in curved geometries. Implemented these algorithms into a flow simulation package "FronTier" in C/C++. The code has been applied to various fluid instability problems: Gravity and shock driven instabilities, turbulent mixing and combustion, and diesel jet flow.
• Conducted a quantitative error and efficiency analysis for the FronTier code.
• Analyzed a scaling law for the shock strength in spherical shock driven mixing.

Computer Simulations for Radiation and Combustion Processes in Star Explosions

• Conducted front tracking simulations for the first spherically diverging, hydrodynamically unstable laboratory experiments of relevance to supernova. Front tracking gave a better agreement with laser experiments than other codes. This work has gained recognition from several leading groups on laser experiments including Lawrence Livermore National Laboratory and University of Michigan.
• Developed radiation-coupled front tracking algorithms in collaboration with laser researchers in University of Michigan.
• Conducted numerical measurement of impact of laser preheat on interface structure and instability.
• Developed numerical models for turbulent combustion in Type Ia supernova. .