This paper uses the provincial panel data from 2011 to 2020 to establish a fixed effect model and a panel threshold model to study the impact of Fintech on the urban-rural income gap. The results show that: (1) Overall, the development of financial technology will significantly narrow the urban-rural income gap, and has heterogeneity. The development of financial technology has the greatest impact on the urban-rural income gap in the western region, followed by the central region, and finally the eastern region; (2) Further establishing a panel threshold model, it is found that different levels of financial technology development have different effects on the urban-rural income gap, and when financial technology develops to a certain extent, its impact on the urban-rural income gap is significantly weakened.

The paper is concerned with a class of stochastic differential equations in infinite dimensional Hilbert space with random coefficients driven by Teugel's martingales which are more general processes. and its optimal control problem. Here Teugels martingales are a family of pairwise strongly orthonormal martingales associated with L\'{e}vy processes (see Nualart and Schoutens). There are three major ingredients. The first is to prove the existence and uniqueness of the solutions by continuous dependence theorem of solutions combining with the parameter extension method. The second is to establish the stochastic maximum principle and verification theorem for our optimal control problem by the classicconvex variation method and dual technique.The third is to represent an example of a Cauchy problem for a controlled stochastic partial differential equation driven by Teugels martingales which our theoretical results can solve.