Abstract
An insurance company holds a responsibility to its consumers and to the general public to maintain its solvency so that the insurance needs of its customers will be met. Insurance is inherently an uncertain business. What level of financial buffer should be held to be sure the business remains solvent and able to pay future claims? This buffer is referred to as the capital and surplus of the company.
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Notes
- 1.
In the US, there are other colored books for other insurers: yellow for property and casualty (general insurance) companies, orange for health insurers, brown for fraternal societies, etc.
- 2.
TVaR is also known as the Conditional Tail Expectation (CTE).
- 3.
Time periods of less than one year would be inconsistent with a one-year timeframe. While, say, quarterly data can be combined into annual effects, it contains more limited data in each period so the volatility is anticipated to increase.
Bibliography or Resources
The field of solvency capital is constantly evolving. Reference material is constantly being updated. I doubt this chapter will prove to be any different. It is written with general concepts in mind. These references the author has found useful in pushing deeper into the concepts and mathematics that are part of this field
International Actuarial Association: Stochastic Modeling: Theory and reality from an actuarial perspective. A strong overall view of stochastic modeling. A good place to start. A lengthy set of references for company specific practice is given in Appendix B (2010)
Klugman, S.A., Panjer, H.H., Willmot, G.E.: Loss models: from data to decisions, 4th edn, The detailed mathematics of many risk distributions is presented with clarity. Used for actuarial education. The art of picking a distribution for a specific risk is a matter for other sources. Wiley (2012)
https://www.wikipedia.org/. This invaluable online reference is a go-to for details about distributions or other mathematics. Its detail on regulatory items is not as strong indicating that going to specific regulatory websites would be preferred
https://en.wikipedia.org/wiki/Copula_(probability_theory). Copulas are commonly used in economic capital work. This reference may serve as an introduction to a topic that will likely require several attempts. The internet is filled with good material
https://eiopa.europa.eu/regulation-supervision/insurance/solvency-ii. Solvency II is a benchmark for all capital work. It is extensive and not always intuitive but when there is no clear path forward for the practitioner, Solvency II provides a “safe harbor”. As stated in the chapter, long-term care insurance is not addressed in solvency II and the use of disability as a substitute is not appropriate
https://www.apra.gov.au/. Australian Prudential Standards are another view of how capital is determined
https://www.thecroforum.org/. The CRO Forum provides up-to-date thinking about various insurance risks. It provides alternatives to Solvency II benchmarks. Of particular interest would be papers on “Calibration recommendation for the correlations in the Solvency II standard formula”, “Scenario Analysis Principles and Practices in the Insurance Industry”, and “Establishing and Embedding Risk Appetite: Practitioners’ View”
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Berger, J.C. (2019). Solvency Capital for Long Term Care Insurance in the United States. In: Dupourqué , E., Planchet, F., Sator, N. (eds) Actuarial Aspects of Long Term Care. Springer Actuarial. Springer, Cham. https://doi.org/10.1007/978-3-030-05660-5_7
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