### Research areas of interest

- Stochastic processes: stochastic calculus, Markov processes, hybrid switching diffusions, martingale methods.
- Mathematical finance and actuarial science: derivatives pricing, stochastic volatility and interest rate modeling, portfolio allocation, indifference pricing, variable annuities, reinsurance.
- 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] - (2018)-
*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.*In Journal of Fixed Point Theory and Applications. [Link] [Preprint] - (2018)
*Explicit solutions to utility maximization problems in a regime-switching market model via Laplace transforms.*In Nonlinear Analysis: Hybrid Systems. [Link] [Preprint] - (2019)
*Assessing Guaranteed Minimum Income Benefits and rationality of exercising reset options in variable annuities.*With R. Jones. In International Journal of Statistics and Probability. [Link] - (2020)
*Integral equation characterization of the Feynman-Kac formula for a regime-switching diffusion.*In Results in Applied Mathematics. [Link].

### Submitted

*Portfolio optimization with a guaranteed minimum maturity benefit and risk-adjusted fees*. With Anne MacKay. [Preprint]

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).