模糊增加與保險自負額

Ambiguity Increases and Insurance Deductibles

本文研究當損失分配不確定下，模糊增加對風險及模糊趨避者之最適保險自負額之影響。自負額是保險理論與實務重要的契約設計。之前研究針對共同保險議題所得結果為偏好相依，惟其應用困難。本文運用α-maxmin 模型證明固定自負額為最適契約；接著假設累積損失機率在原自負額下不變，發現當低於原自負額之損失之可能分配在模糊增加後仍不變，最適選擇不變。若其他設定不變但允許決策者想法集合之中心改變，則發現當最差分配不受影響，但最佳分配以一階隨機優越的概念變差時，最適自負額在模糊增加後變低。若無累積損失機率不變之假設，在原自負額及因模糊趨避扭曲之損失分配下，當獲得部份賠償相較於零賠償的機會在模糊增加後變大時，最適自負額變低。

This paper investigates the impact of an ambiguity increase on the optimal insurance deductible for a risk- and ambiguity-averse individual under the uncertainty of a loss distribution. A deductible is an important insurance contract design in both theory and practice. Previous studies have reported preference-based results in the context of coinsurance, albeit with limited applications. In this paper, we prove a straight deductible is optimal under an α-maxmin model. In the context of the straight deductible, we assume that the cumulative loss probability at an initial optimal deductible is preserved after an ambiguity increase. We show that, for a loss below the initial optimal deductible, the optimal deductible remains unchanged when possible distributions are unaffected by the ambiguity increase. Allowing for a distinct center in the belief set while keeping the others unchanged, we prove that, when the worst distribution is unaffected, but the best distribution deteriorates in terms of first-order stochastic dominance, the optimal deductible becomes lower after the ambiguity increase. If the cumulative loss probability is not preserved, the optimal deductible decreases when, at the initial optimal deductible, the odds of obtaining partial indemnity relative to no indemnity become larger under the loss distribution distorted by ambiguity aversion.