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

Battle Count: 79

Highly relevant to quantitative trading as it addresses the fundamental problem of optimal portfolio allocation when trading costs are nonlinear and transient. The model captures realistic market microstructure features (bid-ask spread dynamics, market resilience, depth). The existence result for optimal strategies under transient price impact is foundational for algorithmic execution and optimal trading. However, the paper is purely theoretical without computational implementation guidance.

The mathematical framework is highly complex, involving non-convex optimization, dynamic programming with non-concave value functions, measurable selection theorems, and sophisticated probability theory. The proof requires careful handling of the non-convexity of the attainable set, backward induction with multiple technical lemmas, and forward verification. Implementing the theoretical results computationally would require significant additional work, as the paper only proves existence without providing constructive algorithms.

As a purely theoretical paper with complete mathematical proofs, reproducibility is assessed by the ability to verify the proofs. All assumptions, lemmas, and theorems are clearly stated with full proofs provided. No computational experiments or code are needed. The mathematical framework is self-contained with references to prior work for foundational results.