Paper: arXiv 2504.18436

Authors: Iman Khajepour, Geoffrey Pritchard, Danny Ralph, Golbon Zakeri

Abstract

We consider a competitive market with risk-averse participants. We assume that agents’ risks are measured by coherent risk measures introduced by Artzner et al. (1999). Fundamental theorems of welfare economics have long established the equivalence of competitive equilibria and system welfare optimization (see, e.g., Samuelson (1947)). These have been extended to the case of risk-averse agents with complete risk markets in Ralph and Smeers (2015). In this paper, we consider risk trading in incomplete markets and introduce a mechanism to complete the market iteratively while monotonically enhancing welfare.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 1.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides rigorous mathematical derivations and convex duality proofs for market completion and social welfare optimization using coherent risk measures. However, it is purely theoretical with zero empirical backtesting or real-world financial data validation.

Research Flowchart

  flowchart TD
    A[Research Goal: Complete incomplete risk markets iteratively while monotonically enhancing welfare] --> B[Inputs: Coherent Risk Measures & Incomplete Market Structure]
    B --> C[Establish Competitive Equilibrium & System Welfare Optimization Models]
    C --> D[Introduce Iterative Market Completion Mechanism]
    D --> E[Simulate Monotone Risk Trading & Efficiency Gains]
    E --> F[Findings: Monotonic Welfare Enhancements & Limit Results for Market Completeness]

Cited References (18)

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  5. The Fundamental Theorems of Modern Welfare Economics, Historically Contemplated. (2007)
  6. Beyond Arbitrage: Good‐Deal Asset Price Bounds in Incomplete Markets (2000)
  7. On the optimality of equilibrium when the market structure is incomplete (1975) — link
  8. Welfare effects of financial innovation in incomplete markets economies with several consumption goods (1995)
and 10 more
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  2. The USSR before the fall: how poor and why (1991)
  3. Energy consumption, capital and real output: A comparison of market and planned economies (1990)
  4. Perturbation analysis of optimization problems (2013)
  5. Probability: theory and examples (2019)
  6. Risk trading and endogenous probabilities in investment equilibria (2015)
  7. Optimization of conditional value-at-risk (2000)
  8. Minimax theorems (1953)
  9. Asymptotic behavior of asset markets: asymptotic inefficiency (1993)
  10. A review of duality theory for linear programming over topological vector spaces (1983) — link

0 of 18 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.