L p Solutions of One-Dimensional Backward Stochastic Differential Equations with Continuous Coefficients

In this article, we study one-dimensional backward stochastic differential equations with continuous coefficients. We show that if the generator f is uniformly continuous in (y, z), uniformly with respect to (t, ω), and if the terminal value ξ ∈L ^p (Ω, ? _T , P) with 1 < p ≤ 2, the backward stochastic differential equation has a unique L ^p solution.