City Research Online

Abstract

This thesis is a collection of three contributions to sensitivity analysis of financial and insurance risk evaluations. Sensitivity analysis constitutes an important component of model building, interpretation and validation, particularly for models whose output is at the core of a risk management decision process. We study models comprising a (random) vector of input factors, an aggregation function mapping input factors to a random output, and a risk measure applied to the output. In most typical insurance and financial applications, the model’s characteristic – a non-analytical and numerically expensive aggregation function evaluated on numerous input factors – renders most sensitivity analysis methodologies unfeasible. We develop sensitivity analysis procedures applicable specifically for the above model setting. First, we address the estimation of risk measures applied to the model output. The fundamental purpose of a risk measure is to distinguish between different risk profiles. However, strong assumptions on the risk measure’s ability to distinguish risk severities lead to non robust estimators. We provide conditions when risk measures exhibit both, robustness and a consistent ranking of risks. Second, we develop a framework termed reverse sensitivity testing, that associates a critical increase in the risk measure to specific input factors. We provide analytical solutions of the stressed distribution of input factors that lead to the required increase in the outputs’ risk measure. Third, we introduce a novel sensitivity measure, which quantifies the extent to which the model output is affected by a stress in an individual input factor. Compared to other sensitivity measures in the literature, the proposed measure incorporates the direct impact of the stressed input as well as indirect effects via other input factors that are dependent on the one being stressed. In this way the dependence between inputs is explicitly taken into account.

Publication Type:	Thesis (Doctoral)
Subjects:	H Social Sciences > HG Finance
Departments:	Bayes Business School Bayes Business School > Actuarial Science & Insurance Doctoral Theses

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