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

O, Hun; Kim, Mun-Chol; Pak, Chol-Gyu

doi:10.5802/crmath.236

Probabilités

Uniqueness of solution to scalar BSDEs with

L exp (μ_{0} \sqrt{2 log (1 + L)})

-integrable terminal values: an

L^{1}

-solution approach

O, Hun ¹ ; Kim, Mun-Chol ¹ ; Pak, Chol-Gyu ¹

¹ Faculty of Mathematics, Kim Il Sung University, Pyongyang, Democratic People’s Republic of Korea

Comptes Rendus. Mathématique, Tome 359 (2021) no. 9, pp. 1085-1095.

Résumé

This paper deals with a class of scalar backward stochastic differential equations (BSDEs) with $L exp (μ_{0} \sqrt{2 log (1 + L)})$ -integrable terminal values for a critical parameter $μ_{0} > 0$ . We show that the solution of these BSDEs is closely connected to the $L^{1}$ -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.

Reçu le : 2021-03-10
Révisé le : 2021-05-03
Accepté le : 2021-06-13
Publié le : 2021-11-03

DOI : 10.5802/crmath.236

Classification : 60H10

Affiliations des auteurs :

O, Hun ¹ ; Kim, Mun-Chol ¹ ; Pak, Chol-Gyu ¹

¹ Faculty of Mathematics, Kim Il Sung University, Pyongyang, Democratic People’s Republic of Korea

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     author = {O, Hun and Kim, Mun-Chol and Pak, Chol-Gyu},
     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},
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     year = {2021},
     doi = {10.5802/crmath.236},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/crmath.236/}
}

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O, Hun; Kim, Mun-Chol; Pak, Chol-Gyu. 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, Tome 359 (2021) no. 9, pp. 1085-1095. doi : 10.5802/crmath.236. http://www.numdam.org/articles/10.5802/crmath.236/

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