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Advances in Heavy Tailed Risk Modeling: A Handbook of Operational Risk by Pavel V. Shevchenko, Gareth W. Peters

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CHAPTEREIGHT

Single Loss Closed-Form Approximations of Risk Measures

This chapter is primarily focussed on the development of closed-form expressions for operational risk (OpRisk) capital and risk measures for loss distribution approach (LDA) models which are generically known as single-loss approximations (SLAs). This chapter naturally extends the asymptotic results for tails of an annual loss distribution developed in Chapter 7 to the quantile asymptotics required for risk measure approximations. To understand why this is of interest, we first discuss the nature of banking and capital accords and the changes that have been occurring in these accords over recent years which motivate one to consider developing such risk-measure-model-based approximation expressions and to study their properties. A more detailed discussion on the regulatory banking accords, their development and context was provided in companion book Cruz et al. (2015, chapters 2, 3 and 4). Before proceeding with this introduction and motivation for SLA development, we state as a summary below a few of the more important key results discussed in detail in this chapter, such as the motivation, definitions and details of these approximations are expanded upon throughout this chapter, and we simply state the results here for convenience to the reader.

8.1 Summary of Chapter Key Results on Single-Loss Risk Measure Approximation (SLA)

The following asymptotic expansions will be obtained as estimates of common risk measures, ...

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