Approximating diffusion reflections at elastic boundaries

Abstract

We show a probabilistic functional limit result for one-dimensional diffusion processes that are reflected at an elastic boundary which is a function of the reflection local time. Such processes are constructed as limits of a sequence of diffusions which are discretely reflected by small jumps at an elastic boundary, with reflection local times being approximated by $\epsilon$-step processes. The construction yields the Laplace transform of the inverse local time for reflection. Processes and approximations of this type play a role in finite fuel problems of singular stochastic control.

arXiv commentTo appear in Electronic Communications in Probability. Modified title and improved readability of some proofs upon referees' comments. arXiv admin note: text overlap with arXiv:1603.06498

References in corpus (1)

• Optimal Liquidation under Stochastic Liquidity