This paper deals with a class of scalar backward stochastic differential equations (BSDEs) with -integrable terminal values for a critical parameter . We show that the solution of these BSDEs is closely connected to the -solution of the BSDEs with integrable parameters. The key tool is the Girsanov theorem. This idea leads to a new approach to the uniqueness of solution and we obtain a new existence and uniqueness result under general assumptions.
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Hun O 1; Mun-Chol Kim 1; Chol-Gyu Pak 1
@article{CRMATH_2021__359_9_1085_0, author = {Hun O and Mun-Chol Kim and Chol-Gyu Pak}, title = {Uniqueness of solution to scalar {BSDEs} with $L\protect \qopname{}{o}{exp}\left(\mu _0\protect \sqrt{2\protect \qopname{}{o}{log}(1+L)}\right)$-integrable terminal values: an $L^1$-solution approach}, journal = {Comptes Rendus. Math\'ematique}, pages = {1085--1095}, publisher = {Acad\'emie des sciences, Paris}, volume = {359}, number = {9}, year = {2021}, doi = {10.5802/crmath.236}, language = {en}, }
TY - JOUR AU - Hun O AU - Mun-Chol Kim AU - Chol-Gyu Pak TI - Uniqueness of solution to scalar BSDEs with $L\protect \qopname{}{o}{exp}\left(\mu _0\protect \sqrt{2\protect \qopname{}{o}{log}(1+L)}\right)$-integrable terminal values: an $L^1$-solution approach JO - Comptes Rendus. Mathématique PY - 2021 SP - 1085 EP - 1095 VL - 359 IS - 9 PB - Académie des sciences, Paris DO - 10.5802/crmath.236 LA - en ID - CRMATH_2021__359_9_1085_0 ER -
%0 Journal Article %A Hun O %A Mun-Chol Kim %A Chol-Gyu Pak %T Uniqueness of solution to scalar BSDEs with $L\protect \qopname{}{o}{exp}\left(\mu _0\protect \sqrt{2\protect \qopname{}{o}{log}(1+L)}\right)$-integrable terminal values: an $L^1$-solution approach %J Comptes Rendus. Mathématique %D 2021 %P 1085-1095 %V 359 %N 9 %I Académie des sciences, Paris %R 10.5802/crmath.236 %G en %F CRMATH_2021__359_9_1085_0
Hun O; Mun-Chol Kim; Chol-Gyu Pak. Uniqueness of solution to scalar BSDEs with $L\protect \qopname{}{o}{exp}\left(\mu _0\protect \sqrt{2\protect \qopname{}{o}{log}(1+L)}\right)$-integrable terminal values: an $L^1$-solution approach. Comptes Rendus. Mathématique, Volume 359 (2021) no. 9, pp. 1085-1095. doi : 10.5802/crmath.236. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.236/
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