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SUMMARY:Stochastic Processes in Domains with Boundaries and Some of Their 
 Financial Applications
DTSTART:20181113T121500
DTEND:20181113T130000
DTSTAMP:20260604T014401Z
UID:f8a59fd99244829d78f8e7f29c090220096532f14eb3ee9a3c13ffb1
CATEGORIES:Conferences - Seminars
DESCRIPTION:Alexander LIPTON\, SilaMoney\, MIT & EPFL\nIn this talk we con
 sider two connected problems:\nFirst\, we study the classical problem of t
 he first passage hitting density of an Ornstein-Uhlenbeck process. We give
  two complementary (forward and backward) formulations of this problem and
  provide semi-analytical solutions for both. The corresponding problems ar
 e comparable in complexity. By using the method of heat potentials\, we sh
 ow how to reduce these problems to linear Volterra integral equations of t
 he second kind. For small values of t we solve these equations analyticall
 y by using Abel equation approximation\; for larger t we solve them numeri
 cally. We also provide a comparison with other known methods for finding t
 he hitting density of interest\, and argue that our method has considerabl
 e advantages and provides additional valuable insights.\nSecond\, we study
  the non-linear diffusion equation associated with a particle system where
  the common drift depends on the rate of absorption of particles at a boun
 dary. We provide an interpretation as a structural credit risk model with 
 default contagion in a large interconnected banking system. Using the meth
 od of heat potentials\, we derive a coupled system of Volterra integral eq
 uations for the transition density and for the loss through absorption. An
  approximation by expansion is given for a small interaction parameter. We
  also present a numerical solution algorithm and conduct computational tes
 ts.
LOCATION:CM 1 113
STATUS:CONFIRMED
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