- 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.
- (2014)- Monotonicity of the value function of a two-dimensional optimal stopping problem. With S. Assing and S. Jacka. In Annals of Applied Probability. [Link] [Preprint]
- (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]
- Commodity options under a regime-switching market model.
- On equity-indexed variable annuities.
- 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).