Page 35 - 36-1

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

*
no indemnity and suffering a large loss between x and D , where the realized loss
F
q
*
is x ∈ [0,D ]. For example, Condition 2 of Proposition 5, Q(x ,1) ≤ 0, is written as
q
F
q
*
for any x ∈ [0,D ]. This means that for an extremely
q
F
*
ambiguity-averse individual with α = 1, at D , the odds of obtaining partial indemnity
F
under the worst loss distribution increase after the general ambiguity increase. Condition 5,
1
1
Q(x , + ε) ≤ 0, is interpreted similarly, but the odds under the ( + ε) -weighted average of
q 2
2
1
the worst and best loss distributions, where 0 < ε ≤ , relate to a non-extremely ambiguity-
2
1
averse individual with α = + ε.
2
We interpret this result using FOC (9). Accompanying a general ambiguity increase,
*
a risk- and ambiguity-averse individual at D experiences higher marginal utility in the
F
loss state covered by partial indemnity under the distorted loss distribution. In particular,
lowering the deductible level after the ambiguity increase raises the net marginal utility
benefit in the indemnified loss state while leaving the expected marginal utility cost in the
uncovered loss state unchanged. Accordingly, after the general ambiguity increase, it is
optimal for the individual to lower the deductible level.
4. Conclusion

This paper provides the determining conditions that raise the optimal insurance
coverage of deductibles after various ambiguity increases. We first prove the optimality

of a straight deductible under the α-maxmin model. Then, the specific, nonspecific,
and general ambiguity increases are examined in turn for a risk- and ambiguity-averse
individual. We focus on the deductible due to its importance and widespread use in both
insurance markets and the insurance literature. Our results are necessary and sufficient.

Furthermore, our conditions in the case of the nonspecific ambiguity increase are
preference-free, thereby facilitating future applications of our findings.
Future research could empirically examine our conditions, and additional determining
conditions could be obtained by considering the insurer’s risk and ambiguity preferences

(e.g., Birghila et al., 2023). Future studies may also consider the nonperformance
ambiguity of the insurance contract, which may impact insurance demand (e.g., Peter and

27