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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