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

Figure 3 An Example of an Ambiguity Increase as Described in Definition 2

Note: In Figure 3, the horizontal axis represents a discrete loss x taking a value in the set of {0,1,2,3}
and the vertical axis represents the cumulative loss probability at each value of x.

3.1 A Specific Ambiguity Increase

In this section, we discuss a specific ambiguity increase that preserves the cumulative
*
loss probability at D . Powers and Tzeng (2001) make a similar assumption on the risk
F
increase in the absence of ambiguity and study its impact on the optimal deductible. In
*
their terminology, we assume that, at D , G(x;π ) and G(x;π ) are stochastically equivalent,
_ T
F
_ F
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meaning that G(x;¯π ) and G(x;¯π ) are stochastically equivalent in this paper. We define
T
F
the specific ambiguity increase as follows.
Definition 3: Under Assumptions 2 and 3, an individual experiences a specific ambiguity
18 Powers and Tzeng (2001) note that a risk change can affect the insurer’s pricing and the optimal
deductible chosen by the insured. They consider a mean-preserving risk increase for the loss above D
*
to ensure that any change in the optimal deductible level purely results from a risk change for the loss
*
below D instead of a price change. Since an ambiguity change does not affect the insurer’s pricing
for the risk in our settings, we do not make this assumption.

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