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 consider a financial model where stocks are available for dynamic trading, and European and American options are available for static trading (semi-static trading strategies). We assume that the American options are infinitely divisible, and can only be bought but not sold. We first get the...

We consider controller-stopper problems in which the controlled processes can have jumps. The global filtration is represented by the Brownian filtration, enlarged by the filtration generated by the jump process. We assume that there exists a conditional probability density function for the jump...

We prove that the perpetual American put option price of level dependent volatility model with compound Poisson jumps is convex and is the classical solution of its associated quasi-variational inequality, that it is C2 except at the stopping boundary and that it is C1 everywhere (i.e. the...

We consider as given a discrete time financial market with a risky asset and options written on that asset and determine both the sub- and super-hedging prices of an American option in the model independent framework of ArXiv:1305.6008. We obtain the duality of results for the sub- and...