ADRIAN ROY L. VALDEZ

Email:  alvaldez@dcs.upd.edu.ph

Research Interests:

    Partial Differential Equations and Its Applications
    Numerical Analysis and Scientific Computing
    Stochastic Analysis
                                            Mathematical Economics and Finance
                                            Mathematical Biology
                                            Mathematical Modeling

Current works:

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.