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Ambiguity Increases and Insurance Deductibles

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decision on optimal insurance coverage or demand for (self-)insurance. Insurance is
an effective tool for transferring risks, and choosing the optimal insurance coverage is a
common decision in daily life. When the risk is ambiguous, the optimal insurance contract
under ambiguity aversion is in a deductible form (e.g., Alary et al., 2013; Gollier, 2014;

Birghila et al., 2023). Furthermore, two streams of research have shown how the optimal
insurance coverage changes with ambiguity aversion and ambiguity increases. One
stream of research shows that greater ambiguity aversion increases the optimal insurance

coverage in both the loss and no-loss states of nature (e.g., Snow, 2011; Alary et al., 2013).
In multiple loss states, depending on how ambiguity is distributed, some papers report
consistent results under certain conditions (e.g., Alary et al., 2013), while other papers
report the opposite result (e.g., Gollier, 2011, 2014). The other stream of research shows
that greater ambiguity increases the optimal insurance coverage under ambiguity aversion

(e.g., Jewitt and Mukerji, 2017; Huang and Tzeng, 2018; Huang, 2025).
In this paper, we focus on the second stream of research, particularly on determining
the conditions under which greater ambiguity leads to higher optimal insurance coverage.

Based on the choices of ambiguity-averse individuals, Jewitt and Mukerji (2017) define
two notions of one act being more ambiguous than another act. Specifically, one notion
is defined by the preference of an ambiguity-averse individual relative to that of an
ambiguity-neutral individual. The other notion is defined by the compensation for giving
up one act for the other act required by a more ambiguity-averse individual compared

to a less ambiguity-averse individual. When these notions are formulated via ambiguity
models such as an α-maxmin model (Ghirardato, Maccheroni, and Marinacci, 2004), the
determining conditions depend on utility functions, which are preference-related. Huang

and Tzeng (2018) define an Nth-degree ambiguity increase as a distribution change in the
sense of an Nth-degree increase in risk (Ekern, 1980). This preserves the mean under a
smooth ambiguity aversion model (Klibanoff, Marinacci, and Mukerji, 2005) and broadens

2 The effect of ambiguity aversion has also been shown on equilibria in insurance markets with
asymmetric information (e.g., Koufopoulos and Kozhan, 2014, 2016; Zheng, Wang, and Li, 2016),
the optimal design for insurance contracts (e.g., Anwar and Zheng, 2012; Alary, Gollier, and Treich,
2013; Gollier, 2014; Birghila, Boonen, and Ghossoub, 2023), and insurance pricing (e.g., Cabantous,
2007; Cabantous, Hilton, Kunreuther, and Michel-Kerjan, 2011; Huang, Huang, and Tzeng, 2013;
Amarante, Ghossoub, and Phelps, 2015; Dietz and Walker, 2019; Dietz and Niehörster, 2021).

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