Paper: arXiv 2610.02863

Authors: Walter Kurz, Reinhard Magg, Florian Kollberg, Wojtek Stricker, Stefan Marx, Frank Reinhardt, Velimir Dedić

Abstract

In private wealth management, a manager delegating to artificial intelligence (AI) acts as the client’s agent and the system’s principal. We introduce a model-independent formulation that combines nested principal–agent delegation with constrained joint maximisation as the task assigned to the AI system. The objective represents client and manager outcomes separately over portfolio–workflow pairs. Legal duties, mandate requirements and evidence sufficiency determine admissibility, with Switzerland, Germany and Austria supplying the legal context. Weights and reference-service floors make the trade-off explicit; concession accounting separates their effects on the client. Analytical constructions and a simulation using public-market observations illustrate the approach. Across eight decision states from four constructed mandates, omitted client liabilities caused two liquidity violations, omitted manager terms caused two capacity violations, and mistranslated weights changed four otherwise admissible choices under faithful optimisation. At the declared weights, six states selected a higher service tier than the client-best alternative, with client concessions of EUR 1,178 to EUR 2,264 and manager gains of EUR 3,062 to EUR 10,381. Three instruction forms each reached all 32 specified decisions under shared numerical, evidence and simulated approval controls; professional instructions matched explicit nested delegation on accuracy and clarification count. Subsequent 2022 exchange-rate and yield paths, combined with constructed growth scenarios, produced lower client outcomes than the reference service although the selected services met the decision-time forecast benchmarks. These examples suggest that the approach could help make mandate choices and their consequences easier to examine. Professional and field studies could assess whether this improves oversight and client outcomes.

Complexity vs Empirical Score

  • Math Complexity: 6.0/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a novel theoretical framework for multi-agent AI in wealth management, grounded in principal-agent theory. It uses analytical constructions and simulations with public market data to illustrate the approach, demonstrating a good balance of mathematical modeling and empirical illustration. The focus on legal and mandate requirements in specific jurisdictions adds a practical and rigorous dimension.

Research Flowchart

  flowchart TD
    A[Research Goal/Question: AI in Private Wealth Management as Nested Principal-Agent Problem?] --> B{Key Methodology Steps: Model-independent formulation, Constrained joint maximization, Concession accounting};
    B --> C[Data/Inputs: Legal duties (CH, DE, AT), Mandate requirements, Evidence sufficiency, Public-market observations, Constructed mandates, Exchange-rate & Yield paths, Growth scenarios];
    C --> D(Computational Processes: Analytical constructions, Simulation, Faithful optimization, Numerical/Evidence/Approval controls);
    D --> E[Key Findings/Outcomes:
        - Omitted liabilities/terms led to liquidity/capacity violations.
        - Mistranslated weights changed choices.
        - Higher service tier selected, with client concessions & manager gains.
        - Professional instructions matched explicit delegation on accuracy/clarification.
        - Lower client outcomes post-2022 due to market conditions despite meeting benchmarks.
        - Approach aids mandate choice examination, potentially improving oversight/outcomes.
    ];