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Research
Computational Finance
The computational finance group is led by Professor Srdjan Stojanovic. His research interests lie in the area of "PDE methods in financial modeling"; more specifically: pricing, hedging, and portfolio optimization. The fundamental relationship between fair pricing and portfolio optimization is emphasized. A variety of financial instruments are studied: equity, bonds, foreign exchange, their derivatives, etc. To that end, a variety of mathematical areas are employed: nonlinear and linear differential equations (partial and ordinary), stochastic differential equations, stochastic control, computational methods (symbolic and numerical), etc.
Faculty
Srdjan Stojanovic, computational finance and nonlinear partial differential equations.
Joanna Mitro, probability and stochastic processes.PhD students
Huaizhou Wang
Jing Liu
Haipeng Tang
Selected Publications
· S.D. Stojanovic, Risk premium and fair option prices under stochastic volatility: the HARA solution, C. R. Acad. Sci. Paris Ser. I 340 (2005) 551-556.
· S.D. Stojanovic, Optimal portfolio series formula under dynamic appreciation rate uncertainty, J. Computational Finance, 8 (2) (2005) 19-54.
· S.D. Stojanovic, Optimal momentum hedging via hypoelliptic reduced Monge-Ampère PDEs, SIAM J. Control & Optimization, 43 (2004) 1151-1173.
· S.D. Stojanovic, Computational Financial Mathematics using Mathematica®: optimal trading in stocks and options, Birkhäuser, Boston, hardcover, xii+481 pp., 2003.
Selected presentations:
· S.D. Stojanovic, Stochastic Volatility & Risk Premium: pricing derivatives, hedging & optimal portfolio management, short course, GARP, London, May 9-10, 2005.
· S.D. Stojanovic, Stochastic Volatility & Risk Premium: pricing derivatives, hedging & optimal portfolio management, short course, GARP, Jersey City, May 2-3, 2005.
· S.D. Stojanovic, Risk premium and fair option prices under stochastic volatility, GARP's 6th Annual Risk Management Convention & Exhibition, February 1-2, 2005, New York City.
· S.D. Stojanovic, Pricing options under stochastic volatility: complete solution, Workshop 8: Model Implementation, Algorithms and Software Issues, IMA, University of Minnesota, May 3-7, 2004.
· S.D. Stojanovic, Options Pricing, Portfolio Hedging, and Data Analysis, short course, IMA, University of Minnesota, March 29, 2004.
· S.D. Stojanovic, Optimal portfolio theories with appreciation rate certainty and appreciation rate uncertainty, AMS-IMS-SIAM Joint Summer Research Conference on Mathematics of Finance, June 22-26, 2003, Snowbird, Utah.