Paper: arXiv 2312.15173

Authors: Zongxia Liang, Jianming Xia, Keyu Zhang

Abstract

This paper considers a class of stochastic control problems with implicitly defined objective functions, which are the sources of time-inconsistency. We study the closed-loop equilibrium solutions in a general controlled diffusion framework. First, we provide a sufficient and necessary condition for a strategy to be an equilibrium. Then, we apply the result to discuss two problems of dynamic portfolio selection for a class of betweenness preferences, allowing for closed convex constraints on portfolio weights and borrowing cost, respectively. The equilibrium portfolio strategies are explicitly characterized in terms of the solutions of some first-order ordinary differential equations for the case of deterministic market coefficients.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous mathematical analysis of equilibrium stochastic control with non-standard preferences, featuring heavy derivations and proofs. However, it is entirely theoretical with no empirical backtesting or real-world dataset validation provided.

Research Flowchart

  flowchart TD
    A[Research Goal: Solve time-inconsistent stochastic control<br/>with implicit objective functions] --> B[Inputs: Controlled diffusion model &<br/>betweenness preferences]
    B --> C[Methodology: Derive necessary & sufficient<br/>conditions for closed-loop equilibrium]
    C --> D[Application: Dynamic portfolio selection with<br/>convex constraints & borrowing costs]
    D --> E[Computation: Solve system of first-order<br/>ordinary differential equations]
    E --> F[Outcomes: Explicit characterization of<br/>equilibrium portfolio strategies]

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1 of 42 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.