A Numerical Scheme for the Quantile Hedging Problem

We consider numerical approximations to the quantile hedging price of a European claim in nonlinear market with Markovian dynamics. study an equivalent stochastic target problem conditional probability success as new state variable, addition asset value process. propose based on piecewise constant policy time stepping coupled novel finite difference schemes. prove convergence monotone case combining backward differential equation arguments Barles and Jakobsen Souganidis approaches for PDEs. The difficulties compared classical setting consist construction schemes under degeneracy due perfectly correlated joint process, unboundedness control effect boundaries variable analysis. extend method class nonmonotone using higher order interpolation linear drivers. In section, we illustrate performance our by considering example financial imperfections, show that standard scheme produces financially counterintuitive solutions.