何種保險單於存在相依背景風險下具有均異效率性？

Which Insurance Policy Is Mean-Variance Efficient with Dependent Background Risk?

本研究測試當存在相依背景風險下，比率保險、自負額保險、上限型保險等三種普遍存在之保險契約形式的均異效率性。本研究考慮被保險人同時面臨隨機的損失與所得，其中所得線性相關於損失。首先，在給定相同保險費的支付下，本研究理論地比較這三種保單的變異數差異。其次，在損失金額服從對數常態分配的假設下，本研究將此三種保險的均異效率前緣繪於同一平面圖；結果顯示，除上限型保險外，自負額保險與比率共保皆可能最有均異效率。其次，若相依背景風險與所得呈負相關，則自付額保險較其餘兩種保險具有均異效率優勢。尤其，當存在正相依背景風險時，適當地組合此三種保單可以提高均異效率。

This study examines the mean-variance efficiencies of three common insurance policies, i.e. proportional coinsurance, deductible, and upper-limit, in the presence of dependent background risk. This study considers an insured who faces simultaneously stochastic loss and income, where the latter is linearly related to the former. First, given the same premium, this study theoretically compares the differences in variance among the three insurance policies. Additionally, the mean-variance frontier curves for the three insurances are depicted on the same graph, assuming the loss obeys a lognormal distribution. This example shows that, although possibly deductible or coinsurance, the efficient insurance policies are not upper-limit. Additionally, in the case where the dependent background risk is negatively related to the income, the deductible insurance always dominates the other two. Particularly, if there exists a positively dependent background risk, an adequate portfolio of the three common insurances may improve the mean-variance efficiency.