# Randomisation with moral hazard: a path to existence of optimal contracts

arXiv: https://arxiv.org/abs/2311.13278 · HTML: https://mlsanity.com/paper/2311.13278/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Nov 2023.

## Built on by (most cited first, 1 of 1)

- [When Should a Human Take Back Control? Optimal Delegation under Turbulent AI Risk](https://mlsanity.com/paper/2609.32083/) (2026)

## Abstract (arXiv)

We study a generic principal-agent problem in continuous time on a finite time horizon. We introduce a framework in which the agent is allowed to employ measure-valued controls and characterise the continuation utility as a solution to a specific form of a backward stochastic differential equation driven by a martingale measure. We leverage this characterisation to prove that, under appropriate conditions, an optimal solution to the principal's problem exists, even when constraints on the contract are imposed. In doing so, we employ compactification techniques and, as a result, circumvent the typical challenge of showing well-posedness for a degenerate partial differential equation with potential boundary conditions, where regularity problems often arise.