March 2024 Wellposedness of anticipated BSDEs with quadratic growth and unbounded terminal value
Ji-Gwon Pak, Mun-Chol Kim, Kon-Gun Kim
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Braz. J. Probab. Stat. 38(1): 108-127 (March 2024). DOI: 10.1214/23-BJPS595


In this paper, we investigate a class of anticipated backward stochastic differential equations (ABSDEs) with quadratic growth and unbounded terminal conditions. ABSDEs give us a duality with stochastic optimal control problems with delay. On the other hand, quadratic ABSDEs can be applied to delayed stochastic linear-quadratic control problems. We prove the well-posedness of ABSDEs with quadratic growth and unbounded terminal values. To obtain the existence result, we first prove a priori estimate for the solutions and then use a limit argument. We also derive a comparison theorem using θ-technique, which gives uniqueness of the solution.


The authors would like to thank the anonymous referees and an Associate Editor for their constructive comments that improved the quality of this paper.


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Ji-Gwon Pak. Mun-Chol Kim. Kon-Gun Kim. "Wellposedness of anticipated BSDEs with quadratic growth and unbounded terminal value." Braz. J. Probab. Stat. 38 (1) 108 - 127, March 2024.


Received: 1 June 2022; Accepted: 1 December 2023; Published: March 2024
First available in Project Euclid: 4 March 2024

MathSciNet: MR4718428
Digital Object Identifier: 10.1214/23-BJPS595

Keywords: Anticipated backward stochastic differential equation , backward stochastic differential equation , quadratic generator , unbounded terminal value

Rights: Copyright © 2024 Brazilian Statistical Association


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Vol.38 • No. 1 • March 2024
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