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NTU Management Review Vol. 36 No. 1 Apr. 2026

Figure 5 An Example of Proposition 4

Note: In Figure 5, the horizontal axis represents a discrete loss x taking a value in the set of
{0,1,2,3,4} and the vertical axis represents the optimal indemnity at each value of x.

the associated set of loss distributions (Δ ) does not have the same center as before (Panel
K
C of Table 1), that is, Assumption 2 is violated. In addition, G(x;π ) and G(x;¯π ) satisfy
K
_ K
Case 2 of Proposition 4. From Figure 5, we can see that the nonspecific ambiguity increase
*
decreases the optimal deductible level to D = 1.99 (the light dashed line).
K
Our determining conditions are comparable to those reported in previous studies
of how risk changes affect a risk-averse individual’s optimal deductible level when the
loss distribution is certain. Eeckhoudt, Gollier, and Schlesinger (1991) show that a mean-
preserving risk change involving FSD deterioration leads to a lower optimal deductible
level if the individual exhibits decreasing or constant absolute risk aversion. Powers and

Tzeng (2001) find the determining conditions for a risk change to decrease the optimal
deductible level under risk aversion. In particular, their determining conditions involve
*
FSD deterioration of the loss distribution below D while preserving the cumulative
*
loss probability at D . Extending this to the case of uncertain loss distributions, we find
analogous determining conditions for a risk- and ambiguity-averse individual under the
similar assumption of the preserving cumulative loss probability made for the specific

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