We study the problem of pricing contingent claims in the presence of uncertainty about the timing and the size of a jump in the price of the underlying. We characterize the price of the claim as the minimal solution of a constrained BSDE and derive a pricing PDE in the special case of a...

This paper relates recursive utility in continuous time to its discrete-time origins and provides a rigorous and intuitive alternative to a heuristic approach presented in [Duffie, Epstein 1992], who formally define recursive utility in continuous time via backward stochastic differential...

We establish a convergence theorem that shows that discrete-time recursive utility, as developed by Kreps and Porteus (1978), converges to stochastic differential utility, as introduced by Duffie and Epstein (1992), in the continuous-time limit of vanishing grid size.