Journées de l'optimisation 2017
HEC Montréal, 810 mai 2017
1^{er} Atelier Canadien sur l'optimisation des soins de santé (CHOW)
HEC Montréal, 1011 mai 2017
JOPT2017
HEC Montréal, 8 — 11 mai 2017
TB5 Méthodes statistiques / Statistical methods
9 mai 2017 10h30 – 12h10
Salle: Nancy et MichelGaucher
Présidée par Martin Cousineau
3 présentations

10h30  10h55
Dynamic programming for valuing American options under variancegamma process
Lévy processes provide a solution to overcome the shortcomings of the lognormal hypothesis. A growing literature proposes the use of purejump Lévy processes such the variancegamma model. In this setting, explicit solutions for derivative prices are unavailable, for instance for the valuation of American options. We propose a dynamic programming approach coupled with finite elements for valuing Americanstyle options under an extended variancegamma model. Our numerical experiments confirm the convergence and show the efficiency of the proposed methodology. We also conduct a numerical investigation that focuses on American options on the S&P 500 futures contracts.

10h55  11h20
A QRFactorizationBased Algorithm for Constrained LeastSquares Problems
We present an interiorpoint method for linear leastsquares problems with both equality and inequality constraints. The algorithm is based on a QR factorization of the leastsquares operator rather than a symmetric indefinite factorization of the KKT matrix to improve numerical stability. We show several formulations of the KKT system and their solution using QR factorization. Numerical results demonstrate the effectiveness of the method.

11h20  11h45
Kernel Mean Matching for Causal Inference
Computing a causal effect from observational data needs to be done carefully in order to obtain an unbiased estimate. In this talk, we give a short introduction to causal inference and to the existing approaches that accomplish this task. We then show how to adapt kernel mean matching, an approach designed for the covariate shift problem in machine learning, in order to compute a causal effect from observational data. We also show how to improve the tuning phase of this approach. We finish by comparing this approach to the stateoftheart using data from a realistic generative model.