Diffusive Limit Approximation of Pure-Jump Optimal Stochastic Control Problems

We consider the diffusive limit of a typical pure-jump Markovian control problem as intensity driving Poisson process tends to infinity. show that convergence speed is provided by Hölder exponent Hessian problem, and explain how correction terms can be constructed. This provides an alternative efficient method for numerical approximation optimal in situations with very high jumps. illustrate this approach context display advertising auction problem.