KTH Matematik |
Tid: 26 januari 2009 kl 15.15-17.00 Plats : Seminarierummet 3733, Institutionen för matematik, KTH, Lindstedts väg 25, plan 7. Karta! Föredragshållare: Adam Andersson, Chalmers Tekniska Högskola. Titel: On weak differentiability of quadratic FBSDEs with application to cross hedging..
Sammanfattning: We present that the solution process Y to a quadratic non-degenerate FBSDE is a member of a local Sobolev space H^{1}_{loc}(R^{m}). The results extends the results on classical differentiability by Imkeller, Ankircher and Dos Reis (2007, "Pricing and hedging of derivatives based on non-tradable underlyings"). Differentiability assumptions, restrictive in applications, has been relaxed. The proof uses results on Dirichlet spaces and SDEs by Bouleau and Hirsch (1989, "On the derivability with respect to the initial data of the solution of a stochastic differential equation with Lipschitz coefficients"). Similar results has been proved by N'Zi, Ouknine and Sulem (2006, "Regularity and representation of viscosity solutions of partial differential equations via backward stochastic differential equations") for FBSDEs with a Lipschitz continuous generator. Applied to mathematical finance an explicit cross hedging strategy can be obtained, expressed in terms of weak gradients of FBSDEs. This makes it possible to write European options on non-tradable indicies. A short introduction to BSDEs will be given, an outline of the proof and something about the application to cross hedging. |
Sidansvarig: Filip Lindskog Uppdaterad: 28/02-2008 |