Insurance demand in the presence of loss‐dependent background risk
分析了当可保损失伴随一个随损失规模增大的不可保零均值背景风险时，保险需求的变化，发现风险脆弱性会引发预防性保险动机并增加最优保险需求。
Abstract We analyze insurance demand when insurable losses come with an uninsurable zero‐mean background risk that increases in the loss size. If the individual is risk vulnerable, loss‐dependent background risk triggers a precautionary insurance motive and increases optimal insurance demand. Prudence alone is sufficient for insurance demand to increase in two cases: the case of fair insurance and the case where the smallest possible loss exceeds a certain threshold value (referred to as the large loss case ). We derive conditions under which insurance demand increases or decreases in initial wealth. In the large loss case, prudence determines whether changes in the background risk lead to more insurance demand. We generalize this result to arbitrary loss distributions and find conditions based on decreasing third‐degree Ross risk aversion, Arrow–Pratt risk aversion, and Arrow–Pratt temperance.