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DROP Function

DROP Function contains several Built-in Multivariate Functions and Solvers.

Component Packages

  • Definition DROP Function Definition Package contains the Function Execution Ancillary Support Objects.

  • E2ERF DROP Function E2ERF Package contains the E2 erf and erf-1 Implementations.

  • E2ERFC DROP Function E2ERFC Package contains the E2 erfc Estimation Function Implementations.

  • ENERF DROP Function ENERF Package contains En erf Series and Generators.

  • Matrix DROP Function Matrix Package contains Support for Functions of Matrices.

  • R1 To R1 DROP Function R1 Package contains several Built-in R1 To R1 Functions.

  • R1 To R1 Solver DROP Function R1 Solver Package contains several Built-in R1 To R1 Solvers.

  • Rd To R1 DROP Function Rd To R1 Package contains the Suite of Built-in Rd To R1 Functions.

  • Rd To R1 Descent DROP Function Rd To R1 Descent Package implements the Suite of Rd To R1 Gradient Descent Techniques.

  • Rd To R1 Solver DROP Function Rd To R1 Solver Package implements the Suite of Built-in Rd To R1 Solvers.

References

  • Abramowitz, M., and I. A. Stegun (2007): Handbook of Mathematics Functions Dover Book on Mathematics

  • Albanese, C., S. Caenazzo, and O. Frankel (2017): Regression Sensitivities for Initial Margin Calculations https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2763488 eSSRN

  • Almgren, R. F., and N. Chriss (2000): Optimal Execution of Portfolio Transactions Journal of Risk 3 (2) 5-39

  • Almgren, R. F. (2009): Optimal Trading in a Dynamic Market https://www.math.nyu.edu/financial_mathematics/content/02_financial/2009-2.pdf

  • Almgren, R. F. (2012): Optimal Trading with Stochastic Liquidity and Volatility SIAM Journal of Financial Mathematics 3 (1) 163-181

  • Andersen and Piterbarg (2010): Interest Rate Modeling (3 Volumes) Atlantic Financial Press

  • Andersen, L. B. G., M. Pykhtin, and A. Sokol (2017): Credit Exposure in the Presence of Initial Margin https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2806156 eSSRN

  • Anfuso, F., D. Aziz, P. Giltinan, and K. Loukopoulus (2017): A Sound Modeling and Back-testing Framework for Forecasting Initial Margin Requirements https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2716279 eSSRN

  • Arfken, G. B., and H. J. Weber (2005): Mathematical Methods for Physicists 6th Edition Harcourt San Diego

  • Armijo, L. (1966): Minimization of Functions having Lipschitz-Continuous First Partial Derivatives Pacific Journal of Mathematics 16 (1) 1-3

  • Bogoliubov, N. N., and D. P. Sankevich (1994): N. N. Bogoliubov and Statistical Mechanics Russian Mathematical Surveys 49 (5) 19-49

  • Boyd, S., and L. van den Berghe (2009): Convex Optimization Cambridge University Press Cambridge UK

  • Caspers, P., P. Giltinan, R. Lichters, and N. Nowaczyk (2017): Forecasting Initial Margin Requirements; A Model Evaluation https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2911167 eSSRN

  • Chang, S. H., P. C. Cosman, L. B. Milstein (2011): Chernoff-Type Bounds for Gaussian Error Function IEEE Transactions on Communications 59 (11) 2939-2944

  • Claerbout, J. F. (1985): Fundamentals of Geo-physical Data Processing Blackwell Scientific

  • Cody, W. J. (1991): Algorithm 715: SPECFUN; A Portable FORTRAN Package of Special Function Routines and Test Drivers ACM Transactions on Mathematical Software 19 (1) 22-32

  • Davis, P. J. (1959): Leonhard Euler's Integral: A Historical Profile of the Gamma Function American Mathematical Monthly 66 (10) 849-869

  • Eustaquio, R., E. Karas, and A. Ribeiro (2008): Constraint Qualification for Nonlinear Programming Federal University of Parana

  • Holubec, V., K. Kroy, and S. Steffenoni (2019): Physically Consistent Numerical Solver for Time-dependent Fokker-Planck Equations Physical Review E 99 (4) 032117

  • Horn, R. A., and C. R. Johnson (1991): Topics in Matrix Analysis Cambridge University Press

  • International Swaps and Derivatives Association (2017): SIMM v2.0 Methodology https://www.isda.org/a/oFiDE/isda-simm-v2.pdf

  • Kadanoff, L. P. (2000): Statistical Physics: Statics, Dynamics, and Re-normalization World Scientific

  • Karush, A. (1939): Minima of Functions of Several Variables with Inequalities as Side Constraints University of Chicago Chicago IL

  • Kuhn, H. W., and A. W. Tucker (1951): Nonlinear Programming Proceedings of the Second Berkeley Symposium University of California Berkeley CA 481-492

  • Nocedal, J., and S. Wright (1999): Numerical Optimization Wiley

  • Ottinger, H. C. (1996): Stochastic Processes in Polymeric Fluids Springer-Verlag Berlin-Heidelberg

  • Rebonato, R., K. McKay, and R. White (2009): The SABR/LIBOR Market Model: Pricing, Calibration, and Hedging for Complex Interest-Rate Derivatives John Wiley and Sons

  • Ruszczynski, A. (2006): Nonlinear Optimization Princeton University Press Princeton NJ

  • Schwerdtfeger, A. (1938): Les Fonctions de Matrices: Les Fonctions Univalentes I Hermann Paris, France

  • Schopf, H. M., and P. H. Supancic (2014): On Burmann Theorem and its Application to Problems of Linear and Non-linear Heat Transfer and Diffusion https://www.mathematica-journal.com/2014/11/on-burmanns-theorem-and-its-application-to-problems-of-linear-and-nonlinear-heat-transfer-and-diffusion/#more-39602/

  • Sylvester, J. J. (1883): On the Equation to the Secular Inequalities in the Planetary Theory The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 16 (100) 267-269

  • Temme N. M. (1996): Special Functions: An Introduction to the Classical Functions of Mathematical Physics 2nd Edition Wiley New York

  • Watson, G. N. (1995): A Treatise on the Theory of Bessel Functions Cambridge University Press

  • Whitaker, E. T., and G. N. Watson (1996): A Course on Modern Analysis Cambridge University Press New York

  • Wikipedia (2019): Bessel Function https://en.wikipedia.org/wiki/Bessel_function

  • Wikipedia (2019): Beta Function https://en.wikipedia.org/wiki/Beta_function

  • Wikipedia (2019): Error Function https://en.wikipedia.org/wiki/Error_function

  • Wikipedia (2019): Fokker-Planck Equation https://en.wikipedia.org/wiki/Fokker%E2%80%93Planck_equation

  • Wikipedia (2019): Gamma Function https://en.wikipedia.org/wiki/Gamma_function

  • Wikipedia (2019): Sylvester Formula https://en.wikipedia.org/wiki/Sylvester%27s_formula

  • Wolfe, P. (1969): Convergence Conditions for Ascent Methods SIAM Review 11 (2) 226-235

  • Wolfe, P. (1971): Convergence Conditions for Ascent Methods; II: Some Corrections SIAM Review 13 (2) 185-188

DROP Specifications