ÃÛÌÒTV

• Finite-state, finite-action Markov Decision process
• Stochastic (Monte Carlo) simulation in pricing financial deritivates

Current research: the development of algorithms for pricing in the absence of full information about the demand process. Typical application: a seller facing repeated selling seasons driven by some fixed demand function that is unknown. Typical model: repeated episodes modelled as a finite-state, finite-action Markov Decision process, whose reward and transition functions are both unknown. Analysis of regret (the expected loss relative to the optimal policy).

Past research projects leading to publications:

Methodological research on stochastic simulation. Primarily, theoretical work on variance reduction methods. Other work has been on the theory of the so-called NORTA method for fitting multivariate discrete distributions with given (rank) correlation structure.

Analysis of Monte Carlo algorithms in finance.  Analysis of convergence of a mesh method for American-option pricing.  Analysis of Monte-Carlo algorithms for option pricing under the variance-gamma model.

Call-center modelling, simulation, and optimization. Modelling of daily call arrivals that accounts for various empirical features (within-day correlation, overdispersion relative to a Poisson model). Call-center performance modelling via continous-time Markov chain approximations. Staffing algorithms based on performance approximations and search methods; simulation-based scheduling algorithms. Modelling call arrivals to an emergency medical center (in Calgary, Canada).