Decision making under uncertainty is prevalent in all human endeavours. The pervasive need to make critical decisions while faced with imperfect knowledge of the future is perhaps most acute in the area of finance. This has resulted in a commensurate demand for tools that allow market participants to analyze and manage their risks effectively. Professor Saunders' research focuses on the application of stochastic optimization and probability, particularly to problems in finance.
Professor Saunders' research on the application of stochastic optimization to finance has covered many topics. These include the use of dual variables from optimal portfolio problems for pricing derivative securities; development of an asset-liability management model for complicated insurance products with embedded options and guarantee provisions; the behaviour of optimal credit portfolios in the "large portfolio" regime that serves as the foundation for current credit risk regulations; efficient computation of optimal portfolios when returns have a Gaussian mixture distribution; and fast algorithms for portfolio optimization using the Omega performance measure.
Recently, Professor Saunders has become interested in problems in credit risk management, as well as the application of analytical techniques to problems in optimal stopping. This has led to work on pricing American options on Levy processes (analysis of the default boundary through integro-differential equations and free boundary problems for integro-differential operators) and inverse default boundary problems (proof of the existence of a default boundary for a given distribution of the time to default, analysis of its small time behaviour, and development of efficient numerical methods for its calculation).
While a graduate student at the University of Toronto, Professor Saunders was an associate member of the Quantitative Research group at Algorithmics Inc., a leading provider of software for financial risk management. He worked on numerous projects including mutual fund ratings, applications of optimization duality to pricing derivative securities, stochastic programming for risk management, and the development of software for a general system for solving financial stochastic optimization problems (a joint project with the University of Cambridge).
After graduation, Professor Saunders was CLR Chair in Corporate Finance and deputy director of RiskLab Cyprus (a financial risk management research laboratory) at the Cyprus International Institute of Management, as well as a research fellow at the HERMES European Center of Excellence on Computational Finance and Economics at the University of Cyprus. He then joined the faculty of the Department of Mathematics at the University of Pittsburgh, where he served as director of the department's Professional Science Masters Program in Mathematical Finance, and supervised numerous collaborative projects between students and financial institutions including RiskMetrics (default boundaries and inverse problems in credit risk), Toronto Dominion Bank (calibration of credit risk models, optimal capital allocation, fast pricing of Bermudan swaptions), PNC Bank (default correlation and CDO pricing, statistical methods for operational risk), and Mellon Bank (mathematical models for operational risk).
Professor Saunders has served as a consultant for many financial institutions including the Bank of Nova Scotia (efficient computation of value at risk for Bermudan swaption portfolios), the Ontario Teachers' Pension Plan (interest rate risk management), the Cyprus Development Bank (credit portfolio management, equity risk management), and the Central Bank of Cyprus (market risk management).
- Rosen, D., and Saunders, D., 2012, CVA the Wrong Way", forthcoming in the Journal of Risk Management for Financial Institutions.
- Chen, X., Cheng, L., Chadam, J., and Saunders, D., 2011, Existence and Uniqueness of the Solution to the Inverse Boundary Crossing Problem for Diffusions. Annals of Applied Probability, 21(5), 1663-1693.
- Garcia-Cespedes, J.C., de Juan Herrero, J.A., Rosen, D., and Saunders, D., 2010, Effective Modelling of Wrong-Way Risk, CCR Capital and Alpha in Basel II, Journal of Risk Model Validation, 4(1), 71-98.
- Marshall, C., Hardy, M., and Saunders, D., 2010, Valuation of a Guaranteed Minimum Income Benefit, North American Actuarial Journal, 14(1), 38-58.
- Rosen, D., and Saunders, D., 2010, Risk Contributions of Systematic Factors in Portfolio Credit Risk Models, Journal of Banking and Finance, 34(2), 336-349.
- Saunders, D., 2009, Pricing Timer Options under Fast Mean-Reverting Stochastic Volatility". Canadian Applied Mathematics Quarterly, 17(4), 737-753.
- Rosen, D., and Saunders, D., 2009, Valuing CDOs of Bespoke Portfolios with Implied Multi-Factor Models, Journal of Credit Risk, 5(3), 3-36.
- Saunders, D., Xiouros, C., and Zenios, S., 2007, Credit Risk Optimization Using Factor Models, Annals of Operations Research, 152(1), 49-77.
- Cheng, L., Chen, X., Chadam, J., and Saunders, D., 2006, Analysis of an Inverse First Passage Problem from Risk Management, SIAM Journal on Mathematical Analysis, 38(3), 845-873.
- Consiglio, A., Saunders, D., and Zenios, S., 2006, Asset and Liability Management for Insurance Products with Minimum Guarantees: The UK Case, Journal of Banking and Finance, 30(2), 645-667.