Paper: arXiv 2304.06938

Authors: Yunhong Li, Zuo Quan Xu, Xun Yu Zhou

Abstract

We study a continuous-time expected utility maximization problem in which the investor at maturity receives the value of a contingent claim in addition to the investment payoff from the financial market. The investor knows nothing about the claim other than its probability distribution, hence an ``intractable claim’’. In view of the lack of necessary information about the claim, we consider a robust formulation to maximize her utility in the worst scenario. We apply the quantile formulation to solve the problem, expressing the quantile function of the optimal terminal investment income as the solution of certain variational inequalities of ordinary differential equations and obtaining the resulting optimal trading strategy. In the case of an exponential utility, the problem reduces to a (non-robust) rank–dependent utility maximization with probability distortion whose solution is available in the literature. The results can also be used to determine the utility indifference price of the intractable claim.

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 presents a rigorous theoretical framework using quantile formulations and variational inequalities to address robust utility maximization with intractable claims. However, it is purely theoretical and lacks empirical backtesting or real-world data validation.

Research Flowchart

  flowchart TD
    A[Goal: Robust Utility Maximization with Intractable Claims] --> B[Inputs: Financial Market & Claim Probability Distribution]
    B --> C[Formulate Worst-Case Scenario Optimization]
    C --> D[Apply Quantile Formulation Method]
    D --> E[Solve Variational Inequalities of ODEs]
    E --> F[Special Case: Reduce Exponential Utility to Rank-Dependent Model]
    E --> G[Outcomes: Optimal Trading Strategy & Utility Indifference Price]
    F --> G