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

the support under the α-maxmin model. Their determining conditions are defined based
on risk and/or ambiguity preferences. These preference-related conditions are difficult
to use in empirical verification and applications. Conversely, Huang (2025) provides
the non-preference-based determining conditions defined as changes in the possible

loss distributions under the α-maxmin model for greater ambiguity, defined as a larger
set of the individual’s beliefs. Nevertheless, the above papers all study the comparative
statics of ambiguity under the problem of optimal coinsurance (optimal portfolio choices,

equivalently) rather than deductibles.
Deductibles are an important aspect of insurance contracts. For example, they
can be used to reduce moral hazard, as is common in automobile and health insurance.
The literature indicates that deductibles are the optimal insurance design for risk and
ambiguity-averse individuals through the smooth ambiguity aversion model (e.g., Alary

et al., 2013; Gollier, 2014). Alary et al. (2013) prove that the straight deductible insurance
is optimal when ambiguity concentrates in the no-loss state of nature. Meanwhile, Gollier
(2014) shows that in multiple states of nature, the optimal insurance design exhibits

different types of deductibles depending on the ambiguity structure. When formulating
the decision-making with a maxmin expected utility (Gilboa and Schmeidler, 1989),
Birghila et al. (2023) demonstrate that the deductible is optimal when the insurer is risk
neutral. Moreover, under the α-maxmin model, Zhang and Li (2021) show that the optimal
3
reinsurance contract is in an excess-of-loss form in certain cases. Overall, to the best
of our knowledge, two areas remain unexamined: whether a straight deductible under
4
the α-maxmin model is still optimal for the insurance contract, and how the optimal
deductible responds to an ambiguity increase. The challenges associated with preference-

based determining conditions and the importance of deductibles motivate us to study
preference-free determining conditions for optimal deductibles under ambiguity.
This paper aims to investigate how the optimal insurance coverage of deductibles
changes and when it increases with an ambiguity increase for a risk- and ambiguity-

3 An excess-of-loss form can be viewed as a form of deductible used in reinsurance contracts. Under a
reinsurance contract with an excess-of-loss form, the reinsurer provides indemnity to the insurer when
the insurer’s claim payments (with respect to the ceded risks) exceed a certain amount or percentage.
4 We thank an anonymous reviewer for raising this point.

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