We analyze an optimal stopping problem with random maturity $\tau_0$ under a nonlinear expectation over a weakly compact set of mutually singular probabilities. The maturity $\tau_0$ is specified as the hitting time to level 0 of some continuous index process $X$ at which the payoff process $Y$...

Given p∈(1,2), we study Lp - solutions of a reflected backward stochastic differential equation with jumps (RBSDEJ) whose generator g is Lipschitz continuous in (y,z,u). We show that such a RBSDEJ with p - integrable parameters admits a unique Lp solution using a fixed-point argument as well...

Given p ∈ (1, 2), we study L^p solutions of a multi-dimensional backward stochastic differential equation with jumps (BSDEJ) whose generator may not be Lipschitz continuous in (y, z, u). We show that such a BSDEJ with a p−integrable terminal data admits a unique L^p solution by approximating...

We apply stochastic Perron's method to a singular control problem where an individual targets at a given consumption rate, invests in a risky financial market in which trading is subject to proportional transaction costs, and seeks to minimize her probability of lifetime ruin. Without relying on...

We show that the value function of a stochastic control problem is the unique solution of the associated Hamilton-Jacobi-Bellman (HJB) equation, completely avoiding the proof of the so-called dynamic programming principle (DPP). Using Stochastic Perron's method we construct a super-solution...