Non-linear non-zero-sum Dynkin games with Bermudan strategies

ArXiv ID: 2311.01086 “View on arXiv”

Authors: Unknown

Abstract

In this paper, we study a non-zero-sum game with two players, where each of the players plays what we call Bermudan strategies and optimizes a general non-linear assessment functional of the pay-off. By using a recursive construction, we show that the game has a Nash equilibrium point.

Keywords: Non-Zero-Sum Game, Bermudan Strategies, Nash Equilibrium, Recursive Construction, Non-Linear Assessment Functional, Derivatives/Contingent Claims

Complexity vs Empirical Score

• Math Complexity: 9.5/10
• Empirical Rigor: 1.0/10
• Quadrant: Lab Rats
• Why: The paper presents a highly abstract, theoretical stochastic game framework with advanced tools like backward stochastic differential equations and nonlinear risk measures, but contains no empirical data, code, or backtesting results.

  flowchart TD
    A["Research Goal: Find Nash Equilibrium in<br>Non-Zero-Sum Dynkin Games with<br>Bermudan Strategies & Non-Linear Payoffs"] --> B["Methodology: Recursive Construction"]
    B --> C["Input: General Non-Linear<br>Assessment Functionals"]
    C --> D["Computational Process:<br>Value Iteration &<br>Fixed Point Analysis"]
    D --> E["Outcome: Proven Existence<br>of Nash Equilibrium"]
    E --> F["Application: Pricing<br>Derivatives/Contingent Claims"]