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NTU Management Review Vol. 36 No. 1 Apr. 2026
Note: In Panel A of Figure 2, the horizontal axis represents a discrete loss taking a value in the set {0, 1, 2, 3, 4, 5} and the
vertical axis represents the cumulative loss probability at each value of . In Panel B of Figure 2, the horizontal axis represents
the discrete loss and the vertical axis represents the optimal indemnity under the loss distributions in Panel A.
3, that is, on the assumption that a straight deductible is optimal. Thus, the problem for
The following comparative statics of an ambiguity increase are based on Proposition 3, that is, on the
the individual is choosing a deductible level D that maximizes ν(I(x);u,z,α,G,π ,¯π ) as choosing a
assumption that a straight deductible is optimal. Thus, the problem for the individual is
_ F
F
F
deductible level that maximizes , , , , , as follows:
follows: � � �
max , , , , ,
�� � �
� �
� � � + 1 �
= �
� � �
� (7)
+ �1 � � � + 1 ��,
�
�
�
�
�
�
(7)
where = 1 + � . Denote as the optimal deductible level
�
* ∗
∗
∗
where . Denote D as the optimal deductible level when
F �
∗
�
�
Π . The FOC is
15
when π ∈ Π . The FOC is
15
F
�
∗
� �
1 + �1 �� � + 1 �
∗
∗
∗
�
�
�
�
�
[1 1+ 1 ] (8)
∗
∗
∗
∗
�
�
�
�
∗
∗
∗
× �1 � � + 1 � =0. (8)
�
�
�
* , 1 1+ 1 must be positive. Based on the left-
∗
∗
∗
*
*
Note that, to drive FOC (8) to zero at D , 1 – (1 + τ)(1 – G(D ;π )) must be positive. Based
Note that, to drive FOC (8) to zero at
�
�
F
F
hand side of FOC (8), lowering the deductible level under the distorted loss distribution could affect two
on the left-hand side of FOC (8), lowering the deductible level under the distorted loss
aspects. The first term on the left-hand side is the expected marginal utility cost in the uncovered loss state
distribution could affect two aspects. The first term on the left-hand side is the expected
due to a higher premium. The second term on the left-hand side is the net marginal utility benefit in the
marginal utility cost in the uncovered loss state due to a higher premium. The second
loss state covered by the partial indemnity due to a higher premium and higher insurance coverage.
term on the left-hand side is the net marginal utility benefit in the loss state covered by the

partial indemnity due to a higher premium and higher insurance coverage.
3. An Ambiguity Increase
We now define an ambiguity increase. Ghirardato et al. (2004) propose the -maxmin model and show
3. An Ambiguity Increase
that the size of the set of probabilities of acts represents the degree of ambiguity perceived by a decision
maker. The larger the set, the greater the ambiguity perceived. Using the maxmin model, Koufopoulos
We now define an ambiguity increase. Ghirardato et al. (2004) propose the α-maxmin
and Kozhan (2014, 2016) define the interval of accident probabilities as the degree of ambiguity to model
model and show that the size of the set of probabilities of acts represents the degree of
ambiguity perceived by a decision maker. The larger the set, the greater the ambiguity

15 Because 0 and 0, � is internal. The second-order condition holds if at the initial deductible level, the individual’s
∗
perceived. Using the maxmin model, Koufopoulos and Kozhan (2014, 2016) define
loss probability density function distorted by ambiguity aversion relative to the insurer’s loss probability density function
is small enough that ���� � � � � ��� � � � � � < 1 + .
�� � � � ∗
16
15 Because u' > 0 and τ > 0, D F is internal. The second-order condition holds if at the initial deductible
*
level, the individual’s loss probability density function distorted by ambiguity aversion relative to the
insurer’s loss probability density function is small enough that < 1 + τ.
17