Wednesday, January 10, 2018 - 16:00 in V3-201
Optimal (financial) position targeting via decoupling fields
A talk in the Bielefeld Stochastic Afternoon - Math Finance Session series by
Stefan Ankirchner from University of Jena
| Abstract: |
In the talk we consider a variant of the basic problem of the
calculus of variations, where the Lagrangian
is convex and subject to randomness adapted to a Brownian filtration. We
solve
the problem by reducing it, via a limiting argument, to an unconstrained
control problem
that consists in finding an absolutely continuous process minimizing the
expected sum
of the Lagrangian and the deviation of the terminal state from a given
target position.
Using the Pontryagin maximum principle one can characterize a solution
of the unconstrained control problem in terms of a fully coupled forward-backward stochastic
differential equation (FBSDE). We use the method of decoupling fields for proving that the
FBSDE has a unique solution.
The talk is based on joint work with Alexander Fromm, Thomas Kruse and
Alexandre Popier.
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