Specific focus of our group includes:
- Basic and applied research in quantitative finance such as pricing and hedging of exotic derivatives, statistical and stochastic modeling of financial instruments and risk and Monte Carlo methods.
- Development of optimal strategies for maximizing revenue while minimizing risk from a variety of investments including foreign exchange risk in a treasury.
- Development of optimal methods for managing risk in non-financial sectors such as energy and commodities as well as risk in human resource management.
- Quantitative study of systemic risk using network theory and dynamical systems and pre- and post-dictive analytics for financial crises.
- Application of machine learning and analytics methods to extract mathematical models from data that are amenable for scenario simulation and optimization and applications of high performance computing.
Some Highlighted Projects
Over the last four years, under the unified umbrella of Quantitative Finance, we have developed theoretical results on pricing and discrete-time hedging of financial derivatives, as well as worked on a computational tool for demonstrating theoretical results. We specifically study applications of optimal hedging problems that we have recently developed for discrete-time hedging, study pricing and hedging in stochastic volatility models, and explore problems related to credit risk and American options.
Financial Risk Mitigation
This project focuses on the quantification of financial risk using suitable risk measures, and the use of numerical stochastic optimization techniques for constructing hedging or trading decisions to mitigate the quantified risk. Specific applications include hedging foreign exchange risk using FX forwards. We are developing a framework for solving such problems numerically for general stochastic models of the risk factors. Testing the idea for different applications and stochastic models and improving its scalability remain a top priority. A separate line of work involves developing models for predicting the credit risk in institutional loans.
Non-Financial Risk Mitigation
In this project, the primary focus is on quantitative methods of risk management for applications other than finance. The specific emphasis will be on formulating appropriate mathematical models for different applications that are amenable to quantitative risk management. The current focus is on two problems, namely:
- Revenue maximization for energy industry
- Optimal human resource management
We are looking forward to applying the know-how developed to insurance and service industry related risk minimization problems.
Systemic Risk and Financial Crises: Theory and Models
We have a strong interest in the quantitative study of systemic risk using combinatorial and dynamical systems-based models. One thread in our current work in this direction involves modeling the dynamics of financial networks taken as a whole. A separate yet related thread involves application of statistical physics based methods to financial crises and validating them with sophisticated data analytics tools.
Model Building and Applications of High Performance Computing
This project focuses on developing techniques for building mathematical models, amenable for simulation and prediction, using historical and real-time data. The first part of the project involves parameter estimation techniques to build statistical time-series or stochastic models from historical data. The second part of the project will focus on developing simulation models based on machine learning techniques with emphasis on transforming descriminator models to models of Markov decision type.
In collaboration with TCS BFS and performance engineering experts we have started extensive investigations around the application of high-performance computing (HPC) to financial risk management problems. Our specific research goal in this direction is to examine the feasibility of the creation of a unified finance platform built on HPC hardware infrastructure.