On integrability of local utility maximizing strategies

By Aleš Černý, Johannes Ruf

Rating

1569
Battle Count: 55

Relevance

8/10
Highly relevant for theoretical foundations of portfolio optimization. Understanding when local optimizers are valid stochastic integrands is crucial for ensuring that derived trading strategies are mathematically well-defined and implementable in continuous-time models.

Implementation Complexity

9/10
Extremely high. The paper involves advanced stochastic calculus, semimartingale characteristics, and convex analysis. Implementing the theoretical checks (like verifying RAE or calculating drift rates of variations) requires significant mathematical expertise and custom numerical solvers.

Reproducibility

3/5
The paper is purely theoretical. All mathematical definitions, theorems, and proofs are fully described within the text. No external data or code is required to verify the theoretical results, but no computational implementation is provided.

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.

Links

arXiv:2610.17915 · Paper rankings

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