Sensitivity of risk measures with respect to the normal approximation of total claim distributions

Arbeitspapier

A simple and commonly used method to approximate the total claim distribution of a (possible weakly dependent) insurance collective is the normal approximation. In this article, we investigate the error made when the normal approximation is plugged in a fairly general distribution-invariant risk measure. We focus on the rate of the convergence of the error relative to the number of clients, we specify the relative error's asymptotic distribution, and we illustrate our results by means of a numerical example. Regarding the risk measure, we take into account distortion risk measures as well as distribution-invariant coherent risk measures.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: SFB 649 Discussion Paper ; No. 2010,033

Classification and Topics

• Classification: Wirtschaft ; Insurance; Insurance Companies; Actuarial Studies ; Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill
• Subject: total claim distribution ; [phi]- and [alpha]-mixing sequences of random variables ; normal approximation ; nonuniform Berry-Esseen inequality ; distortion risk measure ; coherent risk measure ; robust representation ; Risiko ; Messung ; Versicherungstechnisches Risiko ; Statistische Verteilung ; Statistischer Fehler ; Robustes Verfahren ; Theorie

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Krätschmer, Volker ; Zähle, Henryk
• Event: Veröffentlichung
• (who): Humboldt University of Berlin, Collaborative Research Center 649 - Economic Risk
• (where): Berlin
• (when): 2010

Further information

• Handle: http://hdl.handle.net/10419/39297
• Last update: 10.03.2025, 11:42 AM CET