[Paper Review] Risk and Monotone Comparative Statics without Independence

Collin Raymond, Yangwei Song|arXiv (Cornell University)|Jan 15, 2026

Risk and Portfolio Optimization0 citations

TL;DR

Extends monotone comparative statics (MCS) from expected utility to non-expected utility models by using local utility functions. Provides sufficient conditions for MCS and applies to portfolio choice and precautionary savings under diverse non-EU preferences.

ABSTRACT

We extend well-known comparative results under expected utility to models of non-expected utility by providing novel conditions on local utility functions. We illustrate how our results parallel, and are distinct from, existing results for monotone comparative statics under expected utility, as well as risk preferences for non-expected utility. Our conditions generalize existing results for specific preferences (including expected utility) and allow us to verify monotone comparative statics for novel environments and preferences. We apply our results to portfolio choice problems where preferences or wealth might change, as well as precautionary savings.

Motivation & Objective

• Extend well-known MCS results from EU to non-EU risk preferences using local utility functions.
• Develop sufficient conditions under which MCS holds when actions affect distributions or utilities and parameters affect utilities.
• Clarify how non-EU MCS differs from EU results and connect with existing non-EU risk literature.
• Illustrate the framework with portfolio choice and precautionary saving examples.

Proposed method

• Define non-EU preference frameworks using local utility functions u(z,F) and differentiability concepts (Frechet, Hadamard, Gateaux).
• Use Athey (2002)-style MCS logic adapted to non-EU via interval dominance order and SC1/SC2 conditions.
• Express U(x,θ) via V(F) with F determined by x and θ, distinguishing channels through which x and θ affect outcomes or utilities.
• Derive sufficient conditions under which U1(x,θ) is SC1 in θ, U is SC2 in (x,θ), or U is supermodular.
• Leverage lattice-theoretic notions (supermodularity, log-supermodularity) and derivative-based local utilities.
• Apply results to canonical settings like investment choices and precautionary savings.

Experimental results

Research questions

• RQ1 Under non-EU preferences, what conditions on local utilities ensure monotone comparative statics with respect to a parameter θ?
• RQ2 How do three channels—distribution over states, utility function, and monetary payoffs—affect MCS in non-EU models?
• RQ3 Can interval dominance order replace SC2 or stronger conditions to guarantee MCS when using local utilities?
• RQ4 Do standard EU intuitions about DARA and precautionary savings extend to non-EU via local utilities, and when do they fail?
• RQ5 How do the results specialize to portfolio choice and precautionary saving in novel non-EU environments?

Key findings

• Two natural pathways extend EU MCS to non-EU via local utilities: (i) U1(x,θ) SC1 in θ, (ii) U SC2 in (x,θ), with auxiliary conditions.
• Stronger requirements may be needed to preserve MCS under multi-stage aggregation and non-EU primitives.
• Examples show that EU-like conditions on Bernoulli utilities are neither necessary nor sufficient for non-EU MCS; local utilities reveal distinct, position-dependent effects.
• Under RDU, downside risk aversion condition does not perfectly characterize precautionary saving; positive precautionary saving motives can arise even without downside risk aversion.
• The framework nests Machina’s results on investment in risky assets and enables wealth-dependent risk attitudes analyses not captured by EU.
• Applications include precautionary savings and portfolio choices under various non-EU preferences (e.g., rank-dependent, Kreps-Porteus).