Reflected BSDEs and robust optimal stopping for dynamic risk measures with jumps

By Marie Claire Quenez, Agnès Sulem. 2012

83 citations recorded by the source corpus.

We study the optimal stopping problem for dynamic risk measures represented by Backward Stochastic Differential Equations (BSDEs) with jumps and its relation with reflected BSDEs (RBSDEs). The financial position is given by an RCLL adapted process. We first state some properties of RBSDEs with jumps when the obstacle process is RCLL only. We then prove that the value function of the optimal stopping problem is characterized as the solution of an RBSDE. The existence of optimal stopping times is obtained when the obstacle is left-upper semi-continuous along stopping times. Finally, we investigate robust optimal stopping problems related to the case with model ambiguity and their links with mixed control/optimal stopping game problems. We prove that, under some hypothesis, the value function is equal to the solution of an RBSDE. We then study the existence of saddle points when the obstacle is left-upper semi-continuous along stopping times.

Subfields: Demography, Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/1303ebf24aef0632b2d8a172a5de5f9f2bcdafa5

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Demography

1. Peter Imkeller
2. Miryana Grigorova
3. Y. Ouknine
4. Marie Claire Quenez
5. Adrien Richou

In Economics and Econometrics

1. Peter Imkeller
2. Miryana Grigorova
3. Y. Ouknine
4. Marie Claire Quenez
5. Stefan Ankirchner
6. Adrien Richou

In Finance

1. Peter Imkeller
2. Y. Ouknine
3. Miryana Grigorova
4. E. Offen
5. Marie Claire Quenez
6. Alexander Schied
7. Massimiliano Gubinelli
8. Lukasz Delong

Citations in the corpus

• Generalized Dynkin games and doubly reflected BSDEs with jumps (2013, unknown): “3 in [22]) of the solution of a reflected BSDE (associated with an obstacle supposed to be only RCLL), the process (Yt) coincides with the solution of the reflected BSDE associated with the RCLL obstacle (Yt).”
• Optimal stopping with f-expectations: The irregular case (2016, methodology): “Let us note however that the arguments of the proofs given in [36] and in [16] cannot be adapted to our general framework.”
• Reflected BSDEs when the obstacle is not right-continuous and optimal stopping (2015, result): “We thus extend some results of [34] to the case where the optimized process ξ is not cadlag.”