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Ambiguity Increases and Insurance Deductibles

averse individual. Ambiguity comes from the uncertainty of the loss distribution, which
is determined by the individual’s beliefs. We study two types of ambiguity increases:
specific and general. The former refers to an ambiguity increase that broadens the set of
beliefs and preserves a cumulative loss probability at the initial optimal deductible level.

The latter is an ambiguity increase that broadens the set of beliefs without preserving
the requirement of the specific ambiguity increase. We focus on the risk and ambiguity
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aversion of the individual and assume that an insurer is risk and ambiguity neutral. Since
the insurer is ambiguity neutral, the loss distribution in premium pricing is not affected
by the ambiguity increase. Finally, the optimal decisions are formulated by the α-maxmin
model. Commonly employed in the literature, the α-maxmin model and its special case,
the maxmin expected utility, offer several advantages: (1) separating the characterization
of ambiguity from ambiguity preferences; (2) facilitating comparisons with results under

(subjective) expected utility, and (3) accommodating a broader class of model uncertainty
6,7
in decision-making (Birghila et al., 2023).
We first provide a basis for our comparative statics on ambiguity by proving the

optimality of a straight deductible. Then, we obtain necessary and sufficient conditions
defined on the possible loss distributions, which describe how the risk- and ambiguity-
averse individual reacts to the two types of ambiguity increases. After the specific
ambiguity increase, the individual keeps the same deductible level as long as the possible
loss distributions below the initial optimal deductible level remain unaffected. We also

find that the optimal deductible becomes lower after a specific ambiguity increase allows
for a distinct center in the belief set (i.e., a nonspecific ambiguity increase). This occurs

5 Throughout the paper, ambiguity aversion refers to (full) ambiguity aversion. We do not consider the
partial ambiguity aversion (Klingebiel and Zhu, 2023).
6 These two ambiguity models are commonly used in the literature to formulate static insurance
decisions (e.g., Anwar and Zheng, 2012; Koufopoulos and Kozhan, 2014, 2016; Amarante et al.,
2015; Huang and Tzeng, 2018; Dietz and Walker, 2019; Dietz and Niehörster, 2021) and portfolio
choices (e.g., Fei, 2009; Bossaerts, Ghirardato, Guarnaschelli, and Zame, 2010; Epstein and
Schneider, 2010; Jewitt and Mukerji, 2017; Illeditsch et al., 2021).
7 Other ambiguity models have been proposed in the literature, such as the Choquet expected utility
(Schmeidler, 1989), the recursive multiple-priors utility (Epstein and Schneider, 2003), the smooth
ambiguity aversion model, and the local and global multiple-prior representations of ambiguity
(Ghirardato and Siniscalchi, 2012).

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