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The optimal pricing strategy for an insurer when risk preferences are stochastically distributed

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  • Hofmann, Annette
  • Nell, Martin
  • Pohl, Philipp
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    Abstract

    The present paper analyzes the demand for insurance when the insurer has incomplete information about types of potential customers. We assume that customers´ risk preferences cannot be distinguished by the insurer. Therefore, the standard result in insurance economics that the insurer discriminates perfectly in prices cannot be applied. Instead, the present article examines the optimal pricing rule for an insurer faced with stochastic distribution of risk preferences. Within this general model framework, we show that an optimal strategy always exists. Both fixed and proportionate premium loadings (relative to expected loss) are considered. -- Der vorliegende Artikel analysiert die optimale Prämienpolitik eines Versicherers bei stochastischer Verteilung der Nachfragertypen auf Basis einer Preis-Absatz-Funktion. Dem Versicherer ist hier lediglich die Wahrscheinlichkeitsverteilung der individuellen Nachfragertypen bekannt und eine üblicherweise postulierte vollständige Preisdiskriminierung des Versicherers ist daher nicht möglich. Die allgemeine Preis-Absatz-Funktion des Versicherers variiert in Abhängigkeit der verwendeten Modellparameter. Wir zeigen, dass in diesem allgemeinen Modellrahmen stets eine optimale Preispolitik des Versicherers existiert. Dabei wird in Bezug auf den aktuariell fairen Wert der Police sowohl ein fixer als auch ein proportionaler Prämienzuschlag des Versicherers berücksichtigt.

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    File URL: http://econstor.eu/bitstream/10419/54204/1/680536671.pdf
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    Bibliographic Info

    Paper provided by University of Hamburg, Institute for Risk and Insurance in its series Working Papers on Risk and Insurance with number 20.

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    Date of creation: 2007
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    Handle: RePEc:zbw:hzvwps:20

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    Web page: http://www.hzv-uhh.de/
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    Related research

    Keywords: insurance demand; optimal insurance pricing; stochastically distributed risk preferences;

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    1. Kliger, Doron & Levikson, Benny, 1998. "Pricing insurance contracts -- an economic viewpoint," Insurance: Mathematics and Economics, Elsevier, vol. 22(3), pages 243-249, July.
    2. Stiglitz, Joseph E, 1977. "Monopoly, Non-linear Pricing and Imperfect Information: The Insurance Market," Review of Economic Studies, Wiley Blackwell, vol. 44(3), pages 407-30, October.
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