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Title: Sensitivity analysis without repeated model runs Authors:  Andreas Tsanakas - City, University London (United Kingdom) [presenting]
Pietro Millossovich - Cass Business School (United Kingdom)
Silvana Pesenti - Cass Business School (United Kingdom)
Abstract: In risk management, an internal model consists of three elements: (i) a random vector of input risk factors, (ii) a real valued aggregation function, and (iii) the output, which is a random variable obtained by applying the aggregation function on the vector of risk factors. Sensitivity analysis often requires evaluation of changes in the distribution of the output, when the distribution of risk factors is varied with reference to a baseline input distribution. Typically, the distribution of the output is determined via simulation methods. When evaluation of the aggregation function is computationally expensive, as is often the case with models used in practice, extensive sensitivity analyses may become impractical. We propose a method for overcoming this difficulty, by approximating changes in the distribution of the output, while working with a single simulated sample from the baseline model. The method requires knowledge or estimation of the aggregation functions gradient. The approximation is exact when risk factors are independent and gives excellent results when risk factors are not independent, as demonstrated by numerical examples.