Paper: arXiv 2212.04394

Authors: Nicole Bäuerle, An Chen

Abstract

This paper extends the utility maximization literature by combining partial information and (robust) regulatory constraints. Partial information is characterized by the fact that the stock price itself is observable by the optimizing financial institution, but the outcome of the market price of the risk $θ$ is unknown to the institution. The regulator develops either a congruent or distinct perception of the market price of risk in comparison to the financial institution when imposing the Value-at-Risk (VaR) constraint. We also discuss a robust VaR constraint in which the regulator uses a worst-case measure. The solution to our optimization problem takes the same form as in the full information case: optimal wealth can be expressed as a decreasing function of state price density. The optimal wealth is equal to the minimum regulatory financing requirement in the intermediate economic states. The key distinction lies in the fact that the price density in the final state depends on the overall evolution of the estimated market price of risk, denoted as $\hatθ(s)$ or that the upper boundary of the intermediate region exhibits stochastic behavior.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous theoretical contribution to portfolio optimization under partial information and VaR constraints using advanced continuous-time stochastic control. However, it is purely theoretical with no empirical backtesting or real-world dataset validation included in the provided text.

Research Flowchart

  flowchart TD
    A[Research Goal: Optimal Investment under Partial Information & Robust VaR Constraints] --> B[Inputs: Stock Price, Unknown Risk Premium θ, Regulatory Constraints]
    B --> C[Methodology: Estimate Risk Premium θ̂_s & Apply Robust VaR Limits]
    C --> D[Optimization: Solve Utility Maximization via State Price Density]
    D --> E[Key Outcome 1: Wealth equals minimum regulatory requirement in intermediate states]
    D --> F[Key Outcome 2: Final state price density depends on path of estimated risk θ̂_s]