Nonconcave Portfolio Choice under Smooth Ambiguity

2026-03-09

AI Summary

This study addresses continuous-time non-concave portfolio selection under smooth ambiguity, with a focus on nonlinear returns and incentive distortions in delegated portfolio management. To this end, the authors develop a dynamic non-concave asset allocation framework that integrates nonlinear returns, generalized utility functions, and flexible ambiguity attitudes. The approach innovatively combines nonlinear filtering with martingale methods and transforms the ambiguity-averse problem into a dynamically consistent ambiguity-neutral one via a distorted prior. This methodology yields, for the first time under smooth ambiguity, explicit trading rules that unify and generalize classical models with concave or linear returns. Applications demonstrate that ambiguity aversion shifts beliefs toward adverse states, curbs aggressive risk-taking, and effectively reduces portfolio volatility.

Technology Category

• Search and Optimization: Non-convex Optimization
• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

We study continuous-time portfolio choice with nonlinear payoffs under smooth ambiguity and Bayesian learning. We develop a general framework for dynamic, non-concave asset allocation that accommodates nonlinear payoffs, broad utility classes, and flexible ambiguity attitudes. Dynamic consistency is obtained by a robust representation that recasts the ambiguity-averse problem as ambiguity-neutral with distorted priors. This structure delivers explicit trading rules by combining nonlinear filtering with the martingale approach and nests standard concave and linear-payoff benchmarks. As a leading application, delegated management with convex incentives illustrates that ambiguity aversion shifts beliefs toward adverse states, limits the range of states that would otherwise trigger more aggressive risk taking, and reduces volatility through lower risky exposure.

Problem

• portfolio choice
• smooth ambiguity
• nonconcave optimization
• nonlinear payoffs
• Bayesian learning

Innovation

• smooth ambiguity
• nonconcave portfolio choice
• dynamic consistency
• distorted priors
• nonlinear filtering