A note on the Swiss Solvency Test risk measure

Recent theoretical results establish that time-consistent valuations (i.e. pricing operators) can be created by backward iteration of one-period valuations. In this paper we investigate the continuous-time limits of well-known actuarial premium principles when such backward iteration procedures are applied. We show that the one-period variance premium principle converges to the non-linear exponential indifference valuation. Furthermore, we study the convergence of the one-period standard-deviation principle and establish that the Cost-of-Capital principle, which is widely used by the insurance industry, converges to the same limit as the standard-deviation principle. Finally, we study the connections between our time-consistent pricing operators, Good Deal Bound pricing and pricing under model ambiguity.

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“…For a critical discussion on the risk-measure implied by the Swiss Solvency Test we refer toFilipovic and Vogelpoth (2008).…”

mentioning

confidence: 99%

Time-consistent actuarial valuations

Pelsser

Ghalehjooghi

2016

Insurance: Mathematics and Economics

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“…Average Value at Risk plays a prominent role in the Swiss Solvency Test, see e.g. Filipović & Vogelpoth (2008). From a theoretical point of view, it provides the main building block for general distribution-based convex risk measures, as will be explained in Section 7.…”

Section: Average Value At Riskmentioning

confidence: 99%

The Axiomatic Approach to Risk Measures for Capital Determination

Föllmer

Weber

2015

Annu. Rev. Financ. Econ.

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The quantification of downside risk in terms of capital requirements is a key issue for both regulators and the financial industry. This review presents the axiomatic approach, which is based on monetary risk measures. These provide a unifying mathematical framework for the determination of capital requirements, for economic indices of riskiness, and for the analysis of preferences in the face of risk and Knightian uncertainty. In the special case of distribution-based risk measures, we review recent advances in characterizing their statistical properties such as elicitability and robustness.

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“…[35]. Average Value at Risk plays a prominent role in the Swiss Solvency Test; for a careful analysis see Filipović & Vogelpoth [36]. From a theoretical point of view, Average Value at Risk plays a fundamental role in the context of law-invariance, since it provides the building blocks for any law-invariant convex risk measure; this will be explained in Section 5.…”

Section: Average Value At Riskmentioning

confidence: 99%

“…Consider the truncated convex entropic risk measure e γ,c defined in (36). The assumptions of Theorem 7.2 are clearly satisfied.…”

Section: The Convex Casementioning

confidence: 99%