Professor Yuying Li's research interests include the design, analysis and application of computational algorithms for continuous optimization problems and, more generally, problems in scientific computing. She has been working on developing efficient and robust algorithms for various mathematical programming problems. Specifically she has focused on designing methods for solving large scale constrained optimization problems using interior point and trust region approaches. This work includes analysis of theoretical algorithmic properties and development of efficient and robust software. She has also developed algorithms for solving piecewise differentiable optimization problems using an affine scaling approach.
In addition, Li is interested in applying computational methods to practical applications. In recent years, she has been focusing on financial applications.
Fundamental problems in computational finance include the pricing and hedging of financial derivatives. One of the major components of derivative pricing and hedging is calibration of stochastic models. This can be mathematically and computationally challenging since model calibration in finance is often an ill-posed problem due to insufficient market information. Li has been working on developing computationally efficient parametric (as well as non-parametric) methods for robust calibration of stochastic models for option pricing and hedging. Another important problem in computational finance is the determination of optimal trading strategies in a multi-period framework. Li has been interested in efficient computation of optimal portfolios for investment, hedging, and risk management under various risk measures suitable for portfolios including financial derivatives.
Degrees and Awards
BS (Sichuan), MMath, PhD (Waterloo)
David R. Cheriton Fellowship, University of Waterloo (2008-2011)
Industrial and Sabbatical Experience
For the past five years, Li has been an active member of a Cornell-based (now a joint Waterloo / Cornell) finance industry outreach office in lower Manhattan. This group has worked on computational/modeling issues with many companies in the financial services industry (based in New York, Toronto, Tokyo, Hong Kong, and Seoul).
T. Draviam, T. F. Coleman, and Y. Li. Dynamic Liquidation Under Market Impact. To appear in Quantitative Finance, 2010.
S. Moazeni, T. F. Coleman, and Y. Li. Optimal Portfolio Execution Strategies and Sensitivity to Price Impact Parameters. SIAM J. Optimization, Vol 30, pp1620-1654 2010.
L. Zhu, T. F. Coleman, and Y. Li. Min-Max Robust and CVaR Robust Mean-Variance Portfolios. Journal of Risk, Vol 11, 55-85, 2009.
C. He, T. F. Coleman, and Y. Li. Computation and Analysis of a Constrained Entropy Optimization Problem in Finance. Journal of Computational and Applied Mathematics, Vol 222, pp 159-174, 2008.
T. F. Coleman, Y. Kim, Y. Li, and M. Patron. Robustly Hedging Variable Annuities with Guarantees Under Jump and Volatility Risks, Journal of Risk and Insurance, 74:347-376, 2007.
S. Alexander, T. F. Coleman, and Yuying Li. Minimizing VaR and CVaR for a Portfolio of Derivatives, Journal of Banking and Finance, 30(2):583-605, 2006.