Читать книгу Pricing Insurance Risk - Stephen J. Mildenhall - Страница 32

All of the computations we show were completed in Python, R, or a spreadsheet—and sometimes all three. All of the simple discrete examples are easy to replicate in a spreadsheet. There is no conceptual jump from the spreadsheet examples to the R and Python Case Studies, just an increase in the numerical complexity. Once you can implement in a spreadsheet, you understand well enough to program, or instruct a programmer to create, a production implementation.

We implemented the Case Studies using Fast Fourier Transforms (FFTs) because they are fast and precise. You do not have to worry about simulation errors or wait for simulations to complete. The FFT method is described in Wang (1998a) and Mildenhall (2005). FFT methods are extremely powerful but have a fatal flaw: they assume all marginal distributions are independent. For our examples, this flaw is irrelevant. Although the Case Studies assume independent marginals for convenience, all of the methods and algorithms still apply when the marginals are not independent. Its flaw makes FFTs unsuitable for most production applications, and we know that most readers do not use FFTs. Remember: you can implement the Case Studies in any programming language or simulation tool. Just be aware that your answers will vary from those we show due to simulation errors.