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

Figure 4 An Example of a Specific Ambiguity Increase as Described in Definition 3

Note: In Figure 4, the horizontal axis represents a discrete loss x taking a value in the set of
{0,1,2,3,4} and the vertical axis represents the cumulative loss probability at each value of x.

*
*
*
(1) D = D if and only if, ∀x ∈ [0,D ], G(x;π ) = G(x;π ) and G(x;¯π ) =
T
_ F
T
_ T
F
F
G(x;¯π ).
F
*
(2) When Assumption 2 is relaxed so that the center of Δ is not G(x;π ),
T
*
*
*
D ≤ D if and only if, ∀x ∈ [0,D ], G(x;π ) = G(x;π ) and G(x;¯π ) -
F
F
_ T
T
T
_ F
G(x;¯π ) ≥ 0 with strict inequality for some x.
F
Proof: See Appendix D.
Case 1 of Proposition 4 states that, in the face of a specific ambiguity increase, a risk- and
*
ambiguity-averse individual with the α-maxmin preference still chooses D as the optimal
F
*
deductible level when the specific ambiguity increase does not affect losses below D . The
F
*
*
intuition is that, under the deductible D , any losses above D are covered by the insurer
F
F
*
and are therefore treated as an unambiguous risk. In other words, only the loss below D is
F
an ambiguous risk for the individual. Since the specific ambiguity increase has no impact
*
on losses below D , the individual chooses the same deductible level to continue facing an
F
unambiguous risk. This result is consistent with the rationale behind the results reported
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