Diffondo con piacere Mario
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Dear Colleague,
*on Friday, March 14,*
(12:30 noon London, 1:30 pm Berlin, 2:30 pm Helsinki, 8:30 pm Beijing)
in the *International Seminar on SDEs and Related Topics* in Zoom
https://jyufi.zoom.us/j/61891007917
*Laurent Denis* (Université du Maine, France) will speak about
*/BSDE with singular terminal condition: the continuity up to terminal time problem/ *
Abstract: We study the limit behavior of the solution of a backward stochastic differential equation when the terminal condition is singular, that is it can be equal to infinity with a positive probability. In the Markovian setting and in the case where the equation is driven by a Brownian motion, Malliavin's calculus enables us to prove continuity if a balance condition between the growth w.r.t. /y/ and the growth w.r.t. /z/ of the generator is satisfied. We apply our result to liquidity problem in finance and to the solution of some semi-linear partial differential equation ; the imposed assumption is also new in the literature on PDE.
Finally, we prove that if there are jumps (i.e. the operator of the PDE is non local), we observe a propagation of the singularity, contrary to the continuous case (local operator). This talk is based on several joint works with D. Cacitti-Holland and A. Popier.
References: Cacitti-Holland D., Denis L., Popier A. Continuity problem for BSDE and IPDE with singular terminal condition,/Journal of Mathematical Analysis and Applications/, Vol. 543, issue 1 (2025). Cacitti-Holland D., Denis L., Popier A. Growth condition on the generator of BSDE with singular terminal value ensuring continuity up to terminal time, to appear in /Stochastic Processes and their Applications/ (2025).
ABOUT THE SPEAKER:
Laurent Denis is professor at the mathematical laboratory, LMM, of "Le Mans Université" in France, since 2013. Formerly, he was professor at "Université d’Evry » from 2005 to 2013.He received a PhD in Mathematics from University Paris VI in 1994 under the supervision of F. Hirsch and his habilitation from Le Mans University in 2012. From 2012 to 2023 he was also teaching at Ecole Polytechnique. His research interests are centered around uncertain models in finance, non-linear expectation, Stochastic Partial Differential Equations, Malliavin calculus for jump processes, Dirichlet forms and more recently Backward Stochastic Differential equations.. Besides numerous publications, he is the co-author with N. Bouleau of the monograph "Dirichlet Forms Methods for Poisson Point Measures and Lévy Processes » published in 2017.
Welcome in the name of all the organizers
Hannah Geiss For the dates and the list of the upcoming speakers go to http://users.jyu.fi/~chgeiss/seminar-on-sdes.html