Conditional generalized quantiles based on expected utility model and equivalent characterization of properties

Paper: arXiv 2301.12420

Authors: Qinyu Wu, Fan Yang, Ping Zhang

Abstract

As a counterpart to the (static) risk measures of generalized quantiles and motivated by Bellini et al. (2018), we propose a new kind of conditional risk measure called conditional generalized quantiles. We first show their well-definedness and they can be equivalently characterised by a conditional first order condition. We also discuss their main properties, and, especially, We give the characterization of coherency/convexity. For potential applications as a dynamic risk measure, we study their time consistency properties, and establish their equivalent characterizations among conditional generalized quantiles.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 1.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous measure-theoretic mathematical treatment of conditional generalized quantiles and their time-consistency properties. However, it is purely theoretical with no empirical evaluation, market data analysis, or numerical implementation.

Research Flowchart

  flowchart TD
    A[Research Goal: Extend generalized quantiles<br/>to conditional dynamic risk measures] --> B[Input: Static Generalized Quantiles &<br/>Expected Utility Framework]
    B --> C[Formulate Conditional Generalized Quantiles<br/>via Conditional Utility Maximization]
    C --> D[Derive Characterization via<br/>Conditional First-Order Condition]
    D --> E[Analyze Theoretical Properties:<br/>Coherency, Convexity, and Time Consistency]
    E --> F[Outcomes: Well-defined dynamic risk measure<br/>with equivalent characterizations for time consistency]