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NTU Management Review Vol. 36 No. 1 Apr. 2026
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As shown in Appendix E, finding the determining condition under which the general ambiguity
increase lowers the optimal deductible level is equivalent to finding when ) 0 for all 0 ]
ambiguity increase lowers the optimal deductible level is equivalent to finding when ∗
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Q(x,α) ≤ 0 for all x ∈ [0,D ] and α ∈ ( ,1], where Q(x,α) is defined as follows:
and 1], where ) is defined as follows:
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Note that ) is a quadratic function of 0 1] for any 0 ]. Based on this property,
Note that Q(x,α) is a quadratic function of α ∈ [0,1] for any x ∈ [0,D ]. Based on this we
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formulate the following proposition.
property, we formulate the following proposition.
Proposition 5: Suppose that ambiguity preferences can be described by an α-maxmin
Proposition 5. Suppose that ambiguity preferences can be described by an -maxmin model. Under
Assumptions 1–3, a risk- and ambiguity-averse individual experiencing a general
model. Under Assumptions 1–3, a risk- and ambiguity-averse individual
ambiguity increase (as described in Definition 2) lowers the optimal deductible level if
experiencing a general ambiguity increase (as described in Definition 2)
and only if, at any 0 ], there exists ) 0 1] at which )) is a
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lowers the optimal deductible level if and only if, at any x ∈ [0,D ], there
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local maximum or minimum such that one of the following conditions holds for all
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exists α (x ) ∈ [0,1] at which Q(x ,α (x )) is a local maximum or minimum
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(1) + ) 0 when )) is a local maximum at ) 0 ], where
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(1) Q(x , + ε) ≤ 0 when Q(x ,α (x )) is a local maximum at α (x ) ∈ [0, ],
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where 0 < ε ≤ .
(2) 1) 0 when )) is a local minimum at ) 0 ]. 1
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(2) Q(x ,1) ≤ 0 when Q(x ,α (x )) is a local minimum at α (x ) ∈ [0, ].
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(3) )) 0 when )) is a local maximum at ) 1].
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(3) Q(x ,α (x )) ≤ 0 when Q(x ,α (x )) is a local maximum at α (x ) ∈ ( ,1].
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(4) Q(x , + ε) ≤ 0 and Q(x ,1) ≤ 0 when Q(x ,α (x )) is a local minimum at
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(5) + ) q 0 when )) is a local minimum at )=1, where 0 <
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(5) Q(x , + ε) ≤ 0 when Q(x ,α (x )) is a local minimum at α (x ) = 1,
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where 0 < ε ≤ .
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Proof. See Appendix E.
Proof: See Appendix E.
We obtain the determining conditions for reducing the optimal deductible under a general ambiguity
We obtain the determining conditions for reducing the optimal deductible under a h
increase for the five cases in Proposition 5. Each condition applies to a different case depending on whic
general ambiguity increase for the five cases in Proposition 5. Each condition applies to a
different case depending on which interval α (x ) lies in. To provide a better understanding
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of our results, we present the five cases in Panels A–E of Figure 6.
Proposition 5 states that, in the face of a general ambiguity increase, a risk-
and ambiguity-averse individual with the α-maxmin preference chooses a lower
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optimal deductible level than D . This occurs under the distorted loss distribution
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when, at D , the odds of receiving partial indemnity increase compared to facing
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