信息获取与风险厌恶的比较静态分析

中文摘要 AI 辅助

我们研究当决策者面临背景风险并可以在从资产菜单中进行选择之前获取信息时，支付信息意愿如何依赖于风险厌恶。我们区分了投资菜单（其收益与背景财富呈顺周期性）和保险菜单（其收益呈逆周期性）。我们的主要结果表明，资产周期性与背景风险的尾部几何形状之间的相互作用决定了比较静态的方向。当背景风险的密度是对数凹时，对于投资菜单，支付信息意愿随风险厌恶增加而降低；而对于具有向下对数凸背景风险的保险菜单，支付信息意愿随风险厌恶增加而升高。证明比较了有信息和无信息情况下最终财富的分布，并为状态依赖的单交叉比较开发了新的聚合论证。我们还在严格对数凸尾部（针对投资菜单）和超指数左尾（针对保险菜单）下构造了反转情形。

英文摘要

This paper studies how willingness to pay for information depends on risk aversion. We model a decision maker who faces background risk and can acquire information before choosing from a menu of assets. We show that the comparative statics depend on two factors. The first is whether available assets constitute an investment menu, whose payoffs are procyclical with background wealth, or an insurance menu, whose payoffs are countercyclical. The second factor is the tail geometry of background risk. We show that willingness to pay for information decreases with risk aversion for investment menus when the density of background risk is log-concave, and that it increases with risk aversion for insurance menus when background risk is downward-log-convex. The proofs compare the distributions of terminal wealth with and without information. They 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.

发表机构

• Universidad Carlos III（卡洛斯三世大学）
• University of Mannheim（曼海姆大学）
• CNRS – École Polytechnique（法国国家科学研究中心-巴黎综合理工学院）
• Department of Mathematics, London School of Economics（伦敦政治经济学院数学系）
• Brown University（布朗大学）

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