Tiziano De Angelis
Probabilistic Results on Regularity of Optimal Stopping Boundaries
In this talk I will provide an overview of some recent results on probabilistic proofs of continuity and Lipschitz continuity of optimal stopping boundaries in multi-dimensional problems. The probabilistic argument complements some similar results known from the PDE literature concerning free boundary problems, and offers an alternative point of view on the topic. In some instances the methods presented in this talk allow to relax standard assumptions made in the PDE approach, as for example uniform ellipticity of the underlying diffusion. Some applications to models for irreversible investment and actuarial sciences will be illustrated. If time allows I will also connect the regularity of the boundary to questions of smoothness of the value function.
This talk draws from joint work with G. Stabile (Sapienza University of Rome) and ongoing work with G. Peskir (University of Manchester).
References
De Angelis, T. (2015). A note on the continuity of free-boundaries in finite-horizon optimal stopping problems for one dimensional diffusions. SIAM Journal on Control and Optimization 53(1), pp. 167-184.
De Angelis, T., Stabile, G. (2017). On Lipschitz continuous optimal stopping boundaries. Preprint available at http://arxiv.org/abs/1701.07491.
De Angelis, T., Stabile, G. (2017). On the free boundary of an annuity purchase. Preprint available at http://arxiv.org/abs/1707.09494.
De Angelis, T., Peskir, G. (2018). Global C^1 regularity of the value function in optimal stopping problems. Preprint to appear.
Peskir, G. (2017). Continuity of the optimal stopping boundary for two-dimensional diffusions. Preprint available at http://www.maths.manchester.ac.uk/~goran/boundary.pdf.