On the utility problem in a market where price impact is transient

Paper: arXiv 2511.12093

Authors: Lóránt Nagy, Miklós Rásonyi

Abstract

We consider a discrete-time model of a financial market where a risky asset is bought and sold with transactions having a transient price impact. It is shown that the corresponding utility maximization problem admits a solution. We manage to remove some unnatural restrictions on the market depth and resilience processes that were present in earlier work. A non-standard feature of the problem is that the set of attainable portfolio values may fail the convexity property.

Complexity vs Empirical Score

• Math Complexity: 9.5/10
• Empirical Rigor: 1.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper is dense with advanced stochastic calculus, dynamic programming, and non-convex optimization theory, typical of pure mathematical finance. It lacks any data, code, backtests, or empirical implementation details, focusing solely on theoretical existence proofs.

Research Flowchart

  flowchart TD
  A["Research Goal"] -->|Maximize utility in a<br>discrete-time market with<br>transient price impact| B["Model Setup"]
  B -->|Inputs: Discrete-time framework,<br>transient price impact,<br>market depth & resilience| C["Methodology"]
  C -->|Relaxed restrictions on depth<br>and resilience processes| D["Computational Process"]
  D -->|Solve the constrained<br>utility maximization problem| E["Key Findings"]
  E -->|1. Solution exists<br>2. Non-convex attainable set<br>3. Unnatural restrictions removed| F["Outcomes"]
  
  style A fill:#e1f5fe
  style F fill:#e8f5e8