Paper: arXiv 2407.16525

Authors: Luca De Gennaro Aquino, Sascha Desmettre, Yevhen Havrylenko, Mogens Steffensen

Abstract

In intertemporal settings, the multiattribute utility theory of Kihlstrom and Mirman suggests the application of a concave transform of the lifetime utility index. This construction, while allowing time and risk attitudes to be separated, leads to dynamically inconsistent preferences. We address this issue in a game-theoretic sense by formalizing an equilibrium control theory for continuous-time Markov processes. In these terms, we describe the equilibrium strategy and value function as the solution of an extended Hamilton-Jacobi-Bellman system of partial differential equations. We verify that (the solution of) this system is a sufficient condition for an equilibrium and examine some of its novel features. A consumption-investment problem for an agent with CRRA-CES utility showcases our approach.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a highly rigorous continuous-time extension of equilibrium control theory for time-inconsistent Kihlstrom-Mirman preferences using extended HJB equations and verification proofs. However, it is purely theoretical with minimal empirical or numerical implementation, relying primarily on mathematical derivations.

Research Flowchart

  flowchart TD
    A[Research Goal: Address dynamic inconsistency in continuous-time Kihlstrom-Mirman preferences] --> B[Framework: Formalize continuous-time Markov equilibrium control theory]
    B --> C[Derive Extended HJB System of Partial Differential Equations]
    C --> D[Verification Step: Prove HJB solution provides a sufficient condition for equilibrium]
    D --> E[Application / Input: CRRA-CES utility model in a consumption-investment problem]
    E --> F[Key Outcomes: Characterize equilibrium strategies, value functions, and novel preference features]

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