Paper: arXiv 2610.17915

Authors: Aleš Černý, Johannes Ruf

Abstract

In stochastic control problems involving optimal portfolio choice, one often seeks an optimizer of some local criterion (dynamic programming value function) generated by some global criterion (e.g., expected utility). The local optimizer then typically acts as a stochastic integrand with respect to some multivariate stochastic process (e.g., asset prices). This paper takes a closer look at local criteria in the form of ``local expected utility’’. Since the existence of the local optimizer can be established under very mild conditions, it is crucial to understand under what circumstances the local optimizer has good integrability properties. It is shown that the reasonable asymptotic elasticity condition of Kramkov and Schachermayer (1999) applied to the local utility function plays a key role in this context.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: This paper is highly theoretical, focusing on mathematical properties of utility functions and stochastic integrands rather than empirical validation. Its novelty lies in extending the understanding of integrability conditions for local utility maximizing strategies, building upon established theoretical frameworks. The mathematical complexity is very high, but the lack of empirical application places it in the ‘Lab Rats’ quadrant.

Research Flowchart

  flowchart TD
    A[Research Goal: Integrability of Local Utility Maximizing Strategies] --> B{Key Methodology: Analyze "Local Expected Utility" Optimizer};
    B --> C{Inputs: Stochastic Control Problems, Optimal Portfolio Choice Context};
    C --> D[Computational Processes: Analyze Asymptotic Elasticity Condition];
    D --> E{Key Finding: Kramkov-Schachermayer A.E. Condition is Crucial for Integrability};