Paper: arXiv 2505.01876

Authors: Artur Sidorenko

Abstract

We investigate the well-posedness of a general class of singular stochastic control problems in which controls are processes of finite variation. We develop an abstract framework, which we then apply to storage management and portfolio investment problems under proportional transaction costs. Within this setting, we establish the existence of an optimal strategy in the class of randomized controls for a range of goal functionals, including cumulative prospect theory (CPT) preferences. To the best of our knowledge, this is the first treatment of behavioral storage management with the CPT goal functional. For the portfolio management problem, our analysis exploits the metrizable Meyer-Zheng topology to simplify proofs. We thoroughly investigate the applicability of the Skorokhod representation theorem for adapted random processes. Overall, the presented framework provides a clear separation between constraints imposed on the market model and properties required of the goal functional.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 1.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a highly sophisticated, rigorous mathematical framework for singular stochastic control using advanced functional analysis and topology (Meyer-Zheng topology, Skorokhod representation). However, it is purely theoretical with zero empirical validation, backtesting, or real-world data application. Its novelty lies in being the first to combine behavioral Cumulative Prospect Theory (CPT) with storage management under transaction costs.

Research Flowchart

  flowchart TD
    A[Research Goal: Well-posedness of Behavioral Singular Stochastic Control] --> B[Input: Market Model Constraints & Goal Functionals CPT]
    B --> C[Framework: Finite Variation Controls & Meyer-Zheng Topology]
    C --> D[Analysis: Skorokhod Representation Theorem for Adapted Processes]
    D --> E[Applications: Storage Management & Portfolio Investment with Transaction Costs]
    E --> F[Outcome: Existence of Optimal Strategy in Randomized Controls]

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0 of 90 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.