Objectives: Describe the numerical distribution representation and FFT convolution algorithm that underlie all computations in aggregate.
Audience: User who wants a detailed understanding of the computational algorithms, potential errors, options, and parameters.
Prerequisites: Probability theory and aggregate distributions; complex numbers and matrix multiplication; numerical analysis, especially numerical integration; basics of Fourier transforms and series helpful.
See also: :doc:`../2_User_Guides`.
Contents:
- :ref:`num hr`
- :ref:`num overview`
- :ref:`num how agg reps a dist`
- :ref:`num ft convo`
- :ref:`num floats`
Actuarial and operational risk books and papers
- :cite:t:`Gerber1982`
- :cite:t:`Buhlmann1984`
- :cite:t:`Embrechts1993`
- :cite:t:`WangS1998`
- :cite:t:`Grubel1999`
- :cite:t:`Mildenhall2005a`
- :cite:t:`Schaller2008`
- :cite:t:`Kaas2008`
- :cite:t:`Embrechts2009a`
- :cite:t:`Shevchenko2010`
Books on probability covering characteristic functions, t\mapsto \mathsf E[e^{itX}]
- :cite:t:`Loeve1955`
- :cite:t:`feller71`
- :cite:t:`Lukacs1970bk`
- :cite:t:`billingsley`
- :cite:t:`Malliavin1995bk`
- :cite:t:`McKean2014bk`
Books on Fourier analysis and Fourier transforms, t\mapsto \mathsf E[e^{-2\pi itX}], the same concept with slightly different notation. Malliavin is a sophisticated treatment of both Fourier analysis and probability.