What the study found
The study finds a critical wealth level in S-shaped utility maximization with a value-at-risk (VaR, a limit on the chance of losses beyond a set level) constraint and unobservable drift coefficient. This level determines whether the constrained problem has a unique optimal solution and Lagrange multiplier, or is infeasible.
Why the authors say this matters
The authors conclude that their results help characterize when the constrained optimization problem can be solved. They also present algorithms to address the problem and compare them numerically.
What the researchers tested
The researchers studied S-shaped utility maximization under a VaR constraint when the drift coefficient is unobservable. They used a Bayesian filter, the concavification principle, and a change of measure to derive a semi-closed integral representation for the dual value function.
What worked and what didn't
They obtained a semi-closed integral representation for the dual value function. They also identified a critical wealth level that separates cases where the constrained problem admits a unique optimal solution and Lagrange multiplier from cases where it is infeasible. The paper further proposes three solution methods: Lagrange, simulation, and deep neural network, and compares their performance with numerical examples.
What to keep in mind
The abstract does not describe the numerical outcomes in detail, so the relative performance of the three algorithms is not specified here. It also does not provide broader limitations beyond the stated assumptions of VaR constraint and unobservable drift coefficient.
Key points
- A critical wealth level determines whether the constrained problem is solvable or infeasible.
- The model uses S-shaped utility maximization with a value-at-risk constraint.
- The drift coefficient is unobservable, so the study uses Bayesian filtering.
- A semi-closed integral form is derived for the dual value function.
- Three algorithms are proposed: Lagrange, simulation, and deep neural network.
Disclosure
- Research title:
- VaR-constrained utility problem may have a unique solution or be infeasible
- Authors:
- Dongmei Zhu, Ashley Davey, Harry Zheng
- Institutions:
- Imperial College London, Imperial College London, Southeast University
- Publication date:
- 2026-04-25
- OpenAlex record:
- View
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