TY - JOUR
T1 - Anticipated Backward Stochastic Differential Equations with Quadratic Growth
AU - Wen, Jiaqiang
AU - Li, Xun
AU - Hu, Ying
N1 - Funding Information:
Ying Hu was partially supported by Lebesgue Center of Mathematics “Investissements d'avenir” program- ANR-11-LABX-0020-01 , by CAESARS-ANR-15-CE05-0024 and by MFG-ANR16-CE40-0015-01. Xun Li was partially supported by Research Grants Council of Hong Kong under grants 15224215 , 15255416 and 15213218 . Jiaqiang Wen was supported by China Postdoctoral Science Foundation (Grant No. 2019M660968 ) and by National Natural Science Foundation of China (Grant Nos. 11871309 , 11671229 ).
Funding Information:
Ying Hu was partially supported by Lebesgue Center of Mathematics ?Investissements d'avenir? program-ANR-11-LABX-0020-01, by CAESARS-ANR-15-CE05-0024 and by MFG-ANR16-CE40-0015-01. Xun Li was partially supported by Research Grants Council of Hong Kong under grants 15224215, 15255416 and 15213218. Jiaqiang Wen was supported by China Postdoctoral Science Foundation (Grant No. 2019M660968) and by National Natural Science Foundation of China (Grant Nos. 11871309, 11671229).
Publisher Copyright:
© 2020 Elsevier Inc.
PY - 2021/1/5
Y1 - 2021/1/5
N2 - In this paper, we study the solvability of anticipated backward stochastic differential equations (BSDEs, for short) with quadratic growth for one-dimensional case and multi-dimensional case. In these BSDEs, the generator f(.), which is of quadratic growth in Z., involves not only the present information of solution (Y.,Z.) but also its future one. The existence and uniqueness of such BSDEs, under different conditions, are derived for several terminal situations, including small terminal value, bounded terminal value and unbounded terminal value.
AB - In this paper, we study the solvability of anticipated backward stochastic differential equations (BSDEs, for short) with quadratic growth for one-dimensional case and multi-dimensional case. In these BSDEs, the generator f(.), which is of quadratic growth in Z., involves not only the present information of solution (Y.,Z.) but also its future one. The existence and uniqueness of such BSDEs, under different conditions, are derived for several terminal situations, including small terminal value, bounded terminal value and unbounded terminal value.
KW - Anticipated backward stochastic differential equation
KW - Backward stochastic differential equation
KW - Quadratic generator
KW - Time-advanced
UR - http://www.scopus.com/inward/record.url?scp=85091385811&partnerID=8YFLogxK
U2 - 10.1016/j.jde.2020.07.001
DO - 10.1016/j.jde.2020.07.001
M3 - Journal article
SN - 0022-0396
VL - 270
SP - 1298
EP - 1331
JO - Journal of Differential Equations
JF - Journal of Differential Equations
ER -