Controlled one dimensional diffusions with switching costs—average cost criterion

On the Optimal Switching Problem for One-Dimensional Diffusions

We characterize the optimal switching problem as coupled optimal stoping problems. We then use the optimal stopping theory to provide a solution. As opposed to the methods using quasi-variational inequalities and verification theorem we directly work with the value function.

Controlled Switching Diffusions as Hybrid Processes

Numerical methods for controlled regime-switching diffusions and regime-switching jump diffusions

This work is concerned with numerical methods for controlled regime-switching diffusions, and regime-switching jump diffusions. Numerical procedures based on Markov chain approximation techniques are developed. Convergence of the algorithms is derived by means of weak convergence methods. In addition, examples are also provided for demonstration purpose. 2006 Elsevier Ltd. All rights reserved.

Generating integrable one dimensional driftless diffusions

A criterion on the diffusion coefficient is formulated that allows the classification of driftless time and state dependent diffusions that are integrable in closed form via point transformations. In the time dependent and state dependent case, a remarkable intertwining with the inhomogeneous Burger’s equation is exploited. The criterion is constructive. It allows us to devise families of drift...

Wasserstein Decay of One Dimensional Jump-diffusions

This work is devoted to the Lipschitz contraction and the long time behavior of certain Markov processes. These processes diffuse and jump. They can represent some natural phenomena like size of cell or data transmission over the Internet. Using a Feynman-Kac semigroup, we prove a bound in Wasserstein metric. This bound is explicit and optimal in the sense of Wasserstein curvature. This notion ...