Risk and Computation [chapter]

Rüdiger U. Seydel
2015 Innovations in Quantitative Risk Management  
Computation is based on models and applies algorithms. Both a model and an algorithm can be sources of risks, which will be discussed in this paper. The risk from the algorithm stems from erroneous results, the topic of the first part of this paper. We attempt to give a definition of computational risk, and propose how to avoid it. Concerning the underlying model, our concern will not be the "model error". Rather, even the reality (or a perfect model) can be subjected to structural changes:
more » ... inear relations of underlying laws can trigger sudden or unexpected changes in the dynamical behavior. These phenomena must be analyzed, as far they are revealed by a model. A computational approach to such a structural risk will be discussed in the second part. The paper presents some guidelines on how to limit computational risk and assess structural risk. Mathematical Subject Classification 91B30 · 91G60 · 65Y20 · 65P30 Computational Risk Early computer codes concentrated on the evaluation of special functions. The emphasis was to deliver full accuracy (say, seven correct decimal digits on a 32-bit machine) in minimal time. Many of these algorithms are based on formulas of [1, 6] . Later the interest shifted to more complex algorithms such as solving differential equations, where discretizations are required. Typically, the errors are of the type CΔ p , where Δ represents a discretization parameter, p denotes the convergence order of the method, and C is a hardly assessable error coefficient. A control of the error is highly complicated, costly, and frequently somewhat vague, and is source of computational risk.
doi:10.1007/978-3-319-09114-3_17 fatcat:dmwoheedxvay7pqedu6raowlre