Application to Insurance Economics

  • Ulrich Schmidt
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 461)


In the course of this thesis, a bulk of empirical studies have been presenteded which were carried out in terms of laboratory experiments. Although these studies provide many insights into individual decision making under risk, the overall evidence is not unambiguous. A possible response to this fact is to consider field data. The assessment of non-experimental field data is, however, quite difficult because individual preferences are not directly observable. Thus, there is a need for producing testable implications of non-expected utility theories which differ from those of expected utility theory (EU). The goal of this third part is to derive such implications in the context of insurance economics.1


Risk Aversion Expected Utility Risk Averse Indifference Curve Insurance Demand 
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  1. 1.
    Some of the results presented in sections 3.3 and 3.4 already appeared in Schmidt (1996).Google Scholar
  2. 2.
    For further applications of non-expected utility theory to insurance economics cf. Konrad and Skaperdas (1993), Doherty and Eeckhoudt (1995), Diewert (1995), Karni (1995), and Schlee (1995).Google Scholar
  3. 3.
    Although Fréchet-differentiability implies second-order risk aversion the converse is not true. For instance, weighted utility also exhibits second-order risk aversion [cf. Segal and Spivak (1990, p. 119)] but is not Fréchet-differentiable.Google Scholar
  4. 4.
    Cf. Loomes and Segal (1994), p. 239.Google Scholar
  5. 5.
    Cf. Epstein and Zin (1990).Google Scholar
  6. 6.
    Cf. section 1.3.3.Google Scholar
  7. 7.
    Cf. section Scholar
  8. 8.
    For convenience we make a slight change in notation in the third part. From now on, p denotes a single probability and not, as in parts 1 and 2, a probability measure. This allows us to write simply p instead of the more cumbersome p(x).Google Scholar
  9. 9.
    Recall that g(0) = 0 and g(1) = 1.Google Scholar
  10. 10.
    Cf. section Scholar
  11. 11.
    Cf. section It is assumed that preferences satisfy axiom SM.Google Scholar
  12. 12.
    Cf. Gul (1991, p. 675). To be exact, strict risk aversion is also consistent with β = 0. In this case, however, TDA reduces to EU.Google Scholar
  13. 13.
    Note that this definition of g is admissible since g(0) = 0, g(1) = 1, and g is strictly increasing and strictly concave.Google Scholar
  14. 14.
    Cf. Mossin (1968, pp. 556-559), Smith (1968, pp. 70-71), and Ehrlich and Becker (1972, pp. 625-627).Google Scholar
  15. 15.
    See, e.g. Ehrlich and Becker (1972).Google Scholar
  16. 16.
    Cf. Chiang (1984, p. 728).Google Scholar
  17. 17.
    Cf. Fuchs (1976) and Camerer (1989b).Google Scholar
  18. 18.
    This is because a smaller value of p implies a longer interval [1 — g(p), g(p)]. See also Hogarth and Kunreuther (1989).Google Scholar
  19. 19.
    Cf. Gui (1991, p. 676).Google Scholar
  20. 20.
    Cf. Hirshleifer and Riley (1979, p. 1386).Google Scholar
  21. 21.
    For comprehensive surveys of these problems, cf. Winter (1992) and Dionne and Doherty (1992), respectively.Google Scholar
  22. 22.
    Cf. Stiglitz (1983, p. 4).Google Scholar
  23. 23.
    This form of contract is generally called “forcing contract”. Cf. Rees (1987, p. 49).Google Scholar
  24. 24.
    Cf. section 1.3.3.Google Scholar
  25. 25.
    This assumption, in conjunction with p′(a) < 0, allows us to use the first-order approach in the proof of Propositions 3.6–3.8. Cf. Rogerson (1985, pp. 1361-1362). Alternatively, one could also assume that the agent’s choice of a is unique.Google Scholar
  26. 26.
    Note that, according to assumption (i), we have uA > 0 and uB > 0, which implies λ > 0.Google Scholar
  27. 27.
    Cf. Holmstrm (1979, p. 77).Google Scholar
  28. 28.
    Cf. section Scholar
  29. 29.
    For a discussion of this assumption see Shavell (1979a, p. 60, note 14).Google Scholar
  30. 30.
    The argument is taken from Shavell (1979, pp. 59-60).Google Scholar
  31. 31.
    Cf. section 3.1.Google Scholar
  32. 32.
    Note that x and x are unique since uA is strictly increasing.Google Scholar
  33. 33.
    In order to derive this result, one must also assume that “the cost of taking care” is not too high.Google Scholar
  34. 34.
    For analysis in the expected utility framework cf. Spremann (1987, pp. 30-35).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Ulrich Schmidt
    • 1
  1. 1.University of KielInstitut für Finanzwissenschaft und SozialpolitikKielGermany

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