Foschi, Paolo and Pieressa, Luca and Polidoro, Sergio (2008): Parametrix approximations for non constant coefficient parabolic PDEs.
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Abstract
Closed form approximations to the fundamental solution of parabolic PDEs is considered. The approach consists on approximations based on a parametrix series expansion. The approximation error can be bounded by a gaussian function and it is of an order of t^2. These explicit expressions have direct applications in finance and statistics.
Item Type:  MPRA Paper 

Original Title:  Parametrix approximations for non constant coefficient parabolic PDEs 
Language:  English 
Keywords:  parabolic PDE, transition density function, closed form expression, fundamental solution 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C13  Estimation: General G  Financial Economics > G1  General Financial Markets > G12  Asset Pricing ; Trading Volume ; Bond Interest Rates C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C63  Computational Techniques ; Simulation Modeling C  Mathematical and Quantitative Methods > C0  General C  Mathematical and Quantitative Methods > C0  General > C02  Mathematical Methods 
Item ID:  7852 
Depositing User:  Paolo Foschi 
Date Deposited:  21. Mar 2008 06:08 
Last Modified:  02. Mar 2013 06:19 
References:  [1] Milton Abramowitz and Irene A. Stegun, Handbook of mathematical functions with formulas, graphs, and mathematical tables, ninth dover printing, tenth gpo printing ed., National Bureau of Standards Applied Mathematics Series, vol. 55, Dover, 1964. [2] Yacine A ̈ıtSahalia, Maximum likelihood estimation of discretely sampled diffusions: a closedform approximation approach, Econometrica 70 (2002), no. 1, 223–262. [3] F. Corielli and A. Pascucci, Parametrix approximations for option prices, preprint AMS Acta, Universit`a di Bologna (2007). [4] Avner Friedman, Partial differential equations of parabolic type, PrenticeHall Inc., Englewood Cliffs, N.J., 1964. [5] Nancy Makri and William H. Miller, Exponential power series expansion for the quantum time evolution operator, The Journal of Chemical Physics 90 (1989), no. 2, 904–911. [6] L. C. G. Rogers and O. Zane, Sadd lepoint approximations to option prices, Ann. Appl. Probab. 9 (1999), no. 2, 493–503. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/7852 
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