ADRIAN ROY L. VALDEZ
Partial Differential Equations and Its Applications
Numerical Analysis and Scientific Computing
Mathematical Economics and Finance
1. Modeling the Population Dynamics of P. Bahamense
with D. Manansala, R. Talastasin, W. Tan
This research tries to understand the red tide phenomenon by modeling the population dynamics of a phytoplankton named P. Bahamense which takes into account the different life cycles of the said organism. Modeling is done in two ways: one via the construction of a system of ODEs to capture the population dynamics, and; two, thru agent-based modeling.
2. Controllability of de St. Venant Equations
with A. Mendoza, C. Arceo
The de St. Venant equations are used to model behavior of shallow waters. Work is currently being undertaken to prove the existence of controllable boundaries that steer one unsteady flow to another. Existence is also verified via numerical simulations.
3. Pricing a Bermudan Swaption
with D. Villan
This work implements a hybrid pricing algorithm for Bermudan Swaptions combining different paradigms from a "Hull"-based algorithm and a "Brigo"-based one in a setting where time-domain decomposition is non-uniform.
4. Optimal portfolio and utility-indifference pricing and hedging in a regime-switching model
with T. Vargiolu
This research extends the work of Becherer where indifference pricing and hedging was done not only to exponential utilities, but also to logarithmic and hyperbolic absolute risk aversion (HARA) types. Moreover, optimal portfolios were constructed using these three different utility function types.