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The Dynamics of Insurance Prices

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Abstract

We develop a continuous-time general-equilibrium model to rationalise the dynamics of insurance prices in a competitive insurance market with financial frictions. Insurance companies choose underwriting and financing policies to maximise shareholder value. The equilibrium price dynamics are explicit, which allows simple numerical simulations and generates testable implications. In particular, we find that the equilibrium price of insurance is (weakly) predictable and the insurance sector always realises positive expected profits. Moreover, rather than true cycles, insurance prices exhibit asymmetric reversals caused by the reflection of the aggregate capacity process at the dividend and recapitalisation boundaries.

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Notes

  1. Meier (2006).

  2. Meier and Outreville (2006).

  3. Boyer et al. (2012).

  4. See, for example, Cummins and Outreville (1987); Lamm-Tennant and Weiss (1997) or Chen, Wong and Lee (1999).

  5. The notion that external equity financing is more costly than financing via retained earnings is discussed, for example, in Winter (1994). On the empirical side, Gron and Lucas (1998) find evidence of the important costs of raising external capital for the property-casualty insurers.

  6. Stewart (1984).

  7. Bloom (1987).

  8. Cagle and Harrington (1995).

  9. Choi et al. (2002).

  10. Gron (1994).

  11. Winter (1994).

  12. The idiosyncratic part of individual risk is neglected, since it can be eliminated by diversification.

  13. According to Gron and Lucas (1998), for example, the direct costs of equity issues range from 1 to 5 per cent of the value issued.

  14. We assume that reserves earn no interest.

  15. Gerber–Shiu (2004).

  16. Note that u(M) can be interpreted as the market value of one dollar of net worth (book value) in the insurance sector when total capacity is M. It represents the insurance analogue of Tobin’s q ratio, as in Winter (1994).

  17. See, for example, Jeanblanc and Shiryaev (1995), Rochet and Villeneuve (2011), Bolton et al. (2011). In the context of actuarial models, various applications of the optimal liquidity management are discussed in Schmidli (2008).

  18. This property of our model implies that insurance companies always generate non-negative expected profits. In practice, however, loading factors can be negative, as insurers can hedge their losses via complementary financial market activities.

  19. A detailed review of the literature on underwriting cycles can be found in Harrington et al. (2013).

  20. See, for example, Shreve (2004), Chapter 6.4.

  21. See, for example, Ghosh (2010).

  22. Brunnermeier and Sannikov (2014).

  23. Klimenko et al. (2015).

  24. Gerber and Shiu (2004).

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Acknowledgements

We thank Martin Boyer, George Dionne, Mike Hoy, Jean François Outreville, Peter Zweifel and Michael Powers for helpful comments. Nataliya Klimenko and Jean-Charles Rochet gratefully acknowledge financial support from the Swiss Finance Institute and European Research Council under the European Union’s Seventh Framework Program (FP7/2007-2013)/ERC Grant agreement N 249415.

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Henriet, D., Klimenko, N. & Rochet, JC. The Dynamics of Insurance Prices. Geneva Risk Insur Rev 41, 2–18 (2016). https://doi.org/10.1057/grir.2015.5

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