Abstract
| Original language | English |
|---|---|
| Pages (from-to) | 1540-1565 |
| Journal | Stochastic Processes and their Applications |
| Volume | 122 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 2012 |
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Existence, minimality and approximations of solutions of BSDEs with convex drivers. / Cheridito, P.; Stadje, M.A.
In: Stochastic Processes and their Applications, Vol. 122, No. 4, 2012, p. 1540-1565.Research output: Contribution to journal › Article › Scientific › peer-review
TY - JOUR
T1 - Existence, minimality and approximations of solutions of BSDEs with convex drivers
AU - Cheridito, P.
AU - Stadje, M.A.
PY - 2012
Y1 - 2012
N2 - We study the existence of solutions to backward stochastic differential equations with drivers f(t,W,y,z) that are convex in z. We assume f to be Lipschitz in y and W but do not make growth assumptions with respect to z. We first show the existence of a unique solution (Y,Z) with bounded Z if the terminal condition is Lipschitz in W and that it can be approximated by the solutions to properly discretized equations. If the terminal condition is bounded and uniformly continuous in W we show the existence of a minimal continuous supersolution by uniformly approximating the terminal condition with Lipschitz terminal conditions. Finally, we prove the existence of a minimal RCLL supersolution for bounded lower semicontinuous terminal conditions by approximating the terminal condition pointwise from below with Lipschitz terminal conditions.
AB - We study the existence of solutions to backward stochastic differential equations with drivers f(t,W,y,z) that are convex in z. We assume f to be Lipschitz in y and W but do not make growth assumptions with respect to z. We first show the existence of a unique solution (Y,Z) with bounded Z if the terminal condition is Lipschitz in W and that it can be approximated by the solutions to properly discretized equations. If the terminal condition is bounded and uniformly continuous in W we show the existence of a minimal continuous supersolution by uniformly approximating the terminal condition with Lipschitz terminal conditions. Finally, we prove the existence of a minimal RCLL supersolution for bounded lower semicontinuous terminal conditions by approximating the terminal condition pointwise from below with Lipschitz terminal conditions.
U2 - 10.1016/j.spa.2011.12.008
DO - 10.1016/j.spa.2011.12.008
M3 - Article
VL - 122
SP - 1540
EP - 1565
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
SN - 0304-4149
IS - 4
ER -