Page 16 - 36-1

Ambiguity Increases and Insurance Deductibles

2.1 Model Settings
Suppose that there is a risk- and ambiguity-averse individual with initial wealth w and
a potential loss x ∈ [0,L]. The risk is ambiguous in the way that the loss distribution G(x;π)
is determined by the individual’s belief π. A set of π is Π = {π ∣ π ≤ π ≤ ¯π }. In other
F
F
F
words, ambiguity is characterized by Π . In this paper, we assume a simple ambiguity
F
structure where the ambiguity exists for all x, ∈ [0,L] 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
F
distributions when x ∈ Π . Note that, when Π includes only a singleton, the loss
F
F
distribution is certain. In this case, the decision 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 decision-making
9
under ambiguity neutrality, we make the following assumption:
Assumption 1: Under ambiguity neutrality (in the absence of ambiguity), the loss
*
*
distribution is G(x;π ) ∈ Δ , where π ∈ Π .
F
F
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 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 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,
10

8 Gollier (2014) investigates the optimal insurance contract under different ambiguity structures, such
as the ambiguity occurring at the loss below or above the initial optimal deductible level.
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 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

8