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by Π . In this paper, we assume a simple ambiguity structure where the ambiguity exists for all
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to focus on the comparative statics of an ambiguity increase.
8
Let Λ denote a set of all loss distributions and Δ ⊆Λ denote a set of the loss distributions when
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Π . Note that, when Π includes only a singleton, the loss distribution is certain. In this case, the decision
�
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maker faces risk instead of ambiguity since the uncertainty exists only for the loss. Accordingly, the
decision maker behaves as an SEU maximizer, which is consistent with ambiguity neutrality. For
9
decision-making under ambiguity neutrality, we make the following assumption:
Assumption 1. Under ambiguity neutrality (in the absence of ambiguity), the loss distribution is
) Δ , where Π .
∗
∗
�
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To transfer risk, the individual intends to buy an insurance contract from a risk- and ambiguity-neutral
insurer. To focus on the purchasing behavior in response to an ambiguity increase, we assume that the
ambiguity affects the individual only. The insurer is assumed to be risk- and ambiguity-neutral, consistent
NTU Management Review Vol. 36 No. 1 Apr. 2026
with several previous studies on comparative statics (e.g., Snow, 2011; Alary et al., 2013; Gollier, 2014;
Jewitt and Mukerji, 2017; Huang and Tzeng, 2018; Peter and Ying, 2020; Birghila et al., 2023; Huang,
2025). An insurer who prices contracts mainly based on actuarial expertise, experience, and large data can
10
as proven by Birghila et al. (2023) under the maxmin expected utility. Under the insurance
be expected to be risk and ambiguity neutral in premium pricing decision-making. Furthermore, when
the insurer is risk averse, the deductible may not be optimal, as proven by Birghila et al. (2023) under the
contract, the insurer will pay an indemnity denoted by I(x) ≥ 0 to the individual when the
maxmin expected utility. Under the insurance contract, the insurer will pay an indemnity denoted by
loss occurs in the future. For simplicity, we assume the indemnity to be non-negative for
) to the individual when the loss occurs in the future. For simplicity, we assume the indemnity to
all x ∈ [0,L], as in Alary et al. (2013) and Gollier (2014), without being further limited by
be non-negative for all , as in Alary et al. (2013) and Gollier (2014), without being further limited
11
the no-sabotage condition (Birghila et al., 2023).
11
by the no-sabotage condition (Birghila et al., 2023).
The insurance premium paid by the individual (P) is assumed to be actuarially priced
The insurance premium paid by the individual ( ) is assumed to be actuarially priced as an expected
as an expected loss covered with a loading factor τ > 0, which is expressed as
loss covered with a loading factor , which is expressed as
) � ) ). ∗ (1) ( 1 )
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Since the insurer is ambiguity neutral, under Assumption 1, the loss distribution used in
*
the premium pricing is G(x;π ).

8 Gollier (2014) investigates the optimal insurance contract under different ambiguity structures, such as the ambiguity
Under the α-maxmin model, previous works have defined the property of central
occurring at the loss below or above the initial optimal deductible level.
symmetry for the set of the probability measure of state space (Rogers and Ryan, 2012),
9 Without loss of generality, the SEU can represent an ambiguity-neutral preference (e.g., Jewitt and Mukerji, 2017).
10 It is noted that insurers can have different risk and ambiguity attitudes, such as exhibiting ambiguity aversion in the face of
the set of belief associated with the preferences (Jewitt and Mukerji, 2017; Dietz and
ambiguity by charging a higher premium (e.g., Cabantous, 2007; Cabantous et al., 2011). Some researchers study the optimal
insurance coverage when the insurer is risk neutral and ambiguity averse (e.g., Amarante et al., 2015; Dietz and Walker,
Walker, 2019), and the set of the net wealth distributions associated with the beliefs (Huang,
2019; Dietz and Niehörster, 2021) or risk averse (risk neutral) and ambiguity neutral (e.g., Birghila et al., 2023). We
appreciate an anonymous reviewer’s suggestion to justify the assumptions regarding the insurer’s risk and ambiguity
2025). For Δ , we similarly define the central symmetry as follows.
preferences. F
*
Definition 1: The set Δ ⊆ Λ is centrally symmetric if there exists a center G(x;π ) ∈ Δ
11 The no-sabotage condition, which requires the retention to be comonotonic with the indemnity, is imposed on the indemnity
F
F
function in the literature for the non-expected utility to avoid the ex post moral hazard. Birghila et al. (2023) demonstrate
*
where π ∈ Π such that, for any G ∈ Λ, G ∈ Λ if and only if G(x;π ) - [G(x;π)
that the no-sabotage condition affects the shape of the optimal indemnity function. *
F
F
- G(x;π )] ∈ Δ for all x ∈ [0,L]. 7
*
F
12
We illustrate the meaning of Definition 1 with Panel A of Figure 1. Let us consider a
numerical example with the discrete loss x taking a value in the set of {0,1,2,3}. The set Δ
F
has a center G(x;π ), a lower bound G(x;π ), and an upper bound G(x;¯π ). The dark dotted
*
F
_ F
line draws G(x;π ), under which the cumulative loss probabilities of the possible loss
*
and ambiguity averse (e.g., Amarante et al., 2015; Dietz and Walker, 2019; Dietz and Niehörster,
2021) or risk averse (risk neutral) and ambiguity neutral (e.g., Birghila et al., 2023). We appreciate
an anonymous reviewer’s suggestion to justify the assumptions regarding the insurer’s risk and
ambiguity preferences.
11 The no-sabotage condition, which requires the retention to be comonotonic with the indemnity, is
imposed on the indemnity function in the literature for the non-expected utility to avoid the ex post
moral hazard. Birghila et al. (2023) demonstrate that the no-sabotage condition affects the shape of
the optimal indemnity function.
12 We thank an anonymous reviewer for this suggestion.
9