2019/06/25 by Yufeng Shi, Jiaqiang Wen, Shi, Yufeng +3
Economics, Econometrics and Finance · Mathematics · Social Sciences · #60H10 #93E20 #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Nonlinear Differential Equations Analysis #Optimization and Control (math.OC) #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1906.10582
openalex publication_date 2019/06/25 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
Backward doubly stochastic Volterra integral equations (BDSVIEs, for short)\nare introduced and studied systematically. Well-posedness of BDSVIEs in the\nsense of introduced M-solutions is established. A comparison theorem for\nBDSVIEs is proved. By virtue of the comparison theorem, we derive the existence\nof solutions for BDSVIEs with continuous coefficients. Furthermore, a duality\nprinciple between linear (forward) doubly stochastic Volterra integral equation\n(FDSVIE, for short) and BDSVIE is obtained. A Pontryagin type maximum principle\nis also established for an optimal control problem of FDSVIEs.\n