arXiv subjects

A Popier

Publications and source records attributed to A Popier.

2 recordsLinked to original sources

arXiv2016

Limit behaviour of BSDE with jumps and with singular terminal condition

We study the behaviour at the terminal time T of the minimal solution of a backward stochastic differential equation when the terminal data can take the value +$\infty$ with positive probability. In a previous paper, we have proved existence of this minimal solution (in a weak sense) in a quite general setting. But two questions arise in this context and were still open: is the solution c{\`a}d{\`i}{\`a}g on [0,T] ? In other words does the solution have a left limit at time T ? The second question is: is this limit equal to the terminal condition? In this paper, under additional conditions on the generator and the terminal condition, we give a positive answer to these two questions.

math.PR↗

arXiv2015

Minimal supersolutions for BSDEs with singular terminal condition and application to optimal position targeting

We study the existence of a minimal supersolution for backward stochastic differential equations when the terminal data can take the value +$\infty$ with positive probability. We deal with equations on a general filtered probability space and with generators satisfying a general monotonicity assumption. With this minimal supersolution we then solve an optimal stochastic control problem related to portfolio liquidation problems. We generalize the existing results in three directions: firstly there is no assumption on the underlying filtration (except completeness and quasi-left continuity), secondly we relax the terminal liquidation constraint and finally the time horizon can be random.

math.PR↗