Comparative Statics of Information Acquisition and Risk Aversion

2026-09-10

AI Summary

研究了在面临背景风险时，决策者对信息的支付意愿如何随风险厌恶程度变化。通过区分投资菜单和保险菜单，并分析资产周期性与背景风险尾部几何之间的相互作用来解决问题。

Abstract

We study how willingness to pay for information depends on risk aversion when a decision maker faces background risk and can acquire information before choosing from a menu of assets. We distinguish investment menus, whose payoffs are procyclical with background wealth, from insurance menus, whose payoffs are countercyclical. Our main results show that the interaction between asset cyclicality and the tail geometry of background risk determines the direction of the comparative statics. When the density of background risk is log-concave, willingness to pay for information decreases with risk aversion for investment menus, whereas with downward-log-convex background risk it increases with risk aversion for insurance menus. The proofs compare the distributions of terminal wealth with and without information and develop new aggregation arguments for state-dependent single-crossing comparisons. We also construct reversals under strictly log-convex tails for investment menus and super-exponential left tails for insurance menus.

Problem

• information acquisition
• risk aversion
• background risk
• investment menus
• insurance menus

Innovation

• risk aversion
• information acquisition
• background risk
• asset cyclicality
• log-concavity