### Research interests

- Stochastic processes: stochastic calculus, Markov processes, hybrid switching diffusions, martingale methods.
- Mathematical finance: derivatives pricing, stochastic volatility and interest rate modeling, portfolio allocation, indifference pricing.
- Stochastic optimal control: optimal stopping, controlled diffusion processes.

### Publications

- (2014)-
*Monotonicity of the value function of a two-dimensional optimal stopping problem.*With S. Assing and S. Jacka. - (2014)-
*Time-change and control of stochastic volatility.*PhD Thesis. [PDF] - (2017)-
*On the regularity of American options with regime-switching uncertainty.*With S. Jacka. In Stochastic Processes and their Applications. [Link] [Preprint] - (2018)
*Asian option as a fixed-point.*Accepted in Journal of Fixed Point Theory and Applications. - (2018)
*Explicit solutions to utility maximization problems in a regime-switching market model via Laplace transforms.*In Nonlinear Analysis: Hybrid Systems. [Link] [Preprint]

### Working papers

- Commodity options under a regime-switching market model.
- On equity-indexed variable annuities.

Education

- PhD in Statistics (2014), University of Warwick, UK. Time-change and control of stochastic volatility.
- MSc in Mathematics (2009), Universidad de Sonora, Mexico. American option pricing as a free-boundary problem.
- BSc in Mathematics (2007), Universidad de Sonora, Mexico.The Henstock-Kurzweil integral and the Fundamental Theorem of Calculus (in Spanish).