Paper: arXiv 2407.08756

Abstract

We present a number of examples and counterexamples to illustrate the results on cost-efficiency in an incomplete market obtained in [“BS24”]. These examples and counterexamples do not only illustrate the results obtained in [“BS24”], but show the limitations of the results and the sharpness of the key assumptions. In particular, we make use of a simple 3-state model in which we are able to recover and illustrate all key results of the paper. This example also shows how our characterization of perfectly cost-efficient claims allows to solve an expected utility maximization problem in a simple incomplete market (trinomial model) and recover results from [“DS06, Chapter 3”], there obtained using duality.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 1.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents advanced mathematical derivations using convex analysis and optimization theory in incomplete markets, but provides only theoretical examples without any backtesting, datasets, or implementation details.

Research Flowchart

  flowchart TD
  A["Research Goal:<br>Illustrate cost-efficiency<br>in incomplete markets"] --> B["Core Methodology:<br>3-state/Trinomial Model"]
  B --> C["Data/Input:<br>Key Assumptions<br>from [BS24"]]
  C --> D{"Computational Process:<br>Construct Examples<br>& Counterexamples"}
  D --> E{"Analyze Assumptions<br>for Sharpness & Limitations"}
  E --> F["Outcome 1:<br>Validated [BS24"] Results]
  E --> G["Outcome 2:<br>Solved EU Max Problem<br>via Cost-efficiency"]
  F & G --> H["Final Outcome:<br>Connected [BS24"] to<br>["DS06"] Duality Results]