1 School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, and Shandong Key Laboratory of Blockchain Finance, Jinan 250014, China; 2 Institute for Financial Studies and School of Mathematics, Shandong University, Jinan, China; 3 School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China

Abstract A type of infinite horizon forward-backward doubly stochastic differential equations is studied. Under some monotonicity assumptions, the existence and uniqueness results for measurable solutions are established by means of homotopy method. A probabilistic interpretation for solutions to a class of stochastic partial differential equations combined with algebra equations is given. A significant feature of this result is that the forward component of the FBDSDEs is coupled with the backward variable.

Fund:This paper is supported by the National Natural Science Foundation of China (Nos. 11871309, 11671229, 11701040, 61871058, 11871010), Fundamental Research Funds for the Central Universities (2019XD-A11), National Key R&D Program of China (2018YFA0703900), Natural Science Foundation of Shandong Province (Nos. ZR2020MA032, ZR2019MA013), Special Funds of Taishan Scholar Project (tsqn20161041), and by the Fostering Project of Dominant Discipline and Talent Team of Shandong Province Higher Education Institutions.

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