Recent results on bubbles and when European call prices decrease with time
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Date: 02-12-2008
Start Time:
1:00pm
End Time: 2:00pm
Speaker: Philip Protter, Cornell University
Location: Mudd 303
ABSTRACT
Recent developments in the theory of financial bubbles in incomplete markets allows for the possibility of the "birth" of bubbles within the model. We take the approach that the market chooses the risk neutral measure, an idea first proposed by Derman, Dupire, and others. We then allow for the possibility of regime change, where the market moves from one risk neutral measure to another; this allows for bubble birth. We show how unusual events can occur (at least in theory) in the presence of bubbles, such as the a decrease in European call prices as time grows, holding the strike price constant.
The talk is based on joint work with Jean Jacod, Robert Jarrow, Soumik Pal, and Kazuhiro Shimbo.
BIO
Philip Protter received his B.A. from Yale University in 1971 and his Ph.D from the University of California, San Diego in 1975. After teaching at Duke and Purdue University, he joined Cornell in 2000. Protter is currently the Director of the Financial Engineering Program. His research focus is in the area of theoretical and applied probability. Areas of research include mathematical finance theory (asset pricing, liquidity risk, credit risk, etc.), stochastic numerical analysis, stochastic analysis and its applications, weak convergence, Markov process theory, and filtering theory. Protter has a longstanding interest in stochastic calculus and stochastic differential equations. Protter's research focus also encompasses simulation and approximation of solutions for stochastic differential equations.