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CCF Seminar
Umut Cetin London School of Economics Title: Diffusion transformations, BlackScholes equation and optimal stopping Abstract: We develop a new class of path transformations for onedimensional diffusions that are tailored to alter their longrun behaviour from transient to recurrent or vice versa. Apart from their immediate application to the computation of distribution of first exit times, these transformations turn out to be instrumental in resolving the longstanding issue of nonuniqueness for the BlackScholes equations in derivative pricing. Using an appropriate diffusion transformation we show that the properly scaled BlackScholes price is the unique solution of an alternative Cauchy problem. Finally, we use these path transformations to propose a unified framework for solving explicitly the optimal stopping problem for onedimensional diffusions with discounting, which in particular is relevant for the pricing and the optimal exercise boundaries of perpetual American options. Date: Monday, April 3, 2017 Time: 4:30 pm Location: Wean Hall 8220 Submitted by: Dmitry Kramkov 