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WORKING PAPERS:
WORKING PAPERS:
Current version: August 2023 (New version coming soon!).
I study how organizations assign tasks to identify the best candidate to promote among a pool of workers. When only non-routine tasks are informative about a worker’s potential and non-routine tasks are scarce, the organization’s preferred promotion system is an index contest. Each worker is assigned a number that depends only on his own potential. The principal delegates the non-routine task to the worker whose current index is the highest and promotes the first worker whose type exceeds a threshold. Each worker’s threshold depends only on his own type. In this environment, task allocation and workers’ motivation interact through the organization’s promotion decisions. The organization designs the workers’ careers to both screen and develop talent. So competition is mediated by the allocation of tasks: who gets the opportunity to prove themselves is a determinant factor in promotions. Finally, features of the index contest can help understand the prevalence of fast-track promotion, the role of seniority, or when a group of workers is systemically advantaged.
Current version: August 2024.
(Supersedes and expands on Theorem 3 in Smoothness of Value functions in General Control-Stopping Diffusion Problems)
We establish the existence, uniqueness, and W1,2,p-regularity of solutions to fully nonlinear parabolic obstacle problems when the obstacle is the pointwise supremum of arbitrary functions in W1,2,p, and the operator is only assumed to be measurable in the state and time variables. The results hold for a large class of non-smooth obstacles, including all convex obstacles. Applied to stopping problems, they imply that the decision maker never stops at a convex kink of the stopping payoff. The proof relies on new W1,2,p-estimates for obstacle problems where the obstacle is the maximum of finitely many functions in W1,2,p.
Current version: August 2024.
How do decisions change with the economic environment and with time? This paper studies general nonstationary stopping problems and provides the methodological tools to answer these questions. First, we identify conditions that ensure a monotone relation between decisions’ timing and outcomes. These conditions apply to a prevalent class of economic environments. Second, we develop a theory of monotone comparative statics for stopping problems, offering general and unifying qualitative insights into the decision-maker’s value and stopping behavior. We apply our results to models of information acquisition, bankruptcy, irreversible investment, and option pricing to explain documented patterns at odds with current theories.
Current version: November 2022 (New version coming soon!).
We derive properties of value functions in mixed optimal control and stopping problems in which (i) the state variable may be multi-dimensional, (ii) the domain may be unbounded and irregular, and (iii) primitives may be time-dependent. We show that the value function is the unique Lp-solution of the Hamilton-Jacobi-Bellman equation and that it is twice parabolically differentiable a.e. and continuously differentiable in the state variable under general conditions that accommodate most economic applications. We show that the smooth-pasting property must hold everywhere with respect to all non-time variables and provide sufficient conditions under which smooth pasting must also hold with respect to time. Our results imply that numerical solutions obtained by standard methods converge uniformly to the value function.
Current version: February 2025.
We study the robust regulation of labour contracts in moral hazard problems. A firm offers a contract to incentivise a worker protected by limited liability. A regulator chooses the set of permissible contracts to (i) improve efficiency and (ii) protect the worker. The regulator does not know the worker’s actions and the firm’s costs and evaluates regulations by their worst-case regret. The regret-minimising regulation imposes a minimum piece rate compensation for the worker: it allows all contracts above a minimum linear contract. The slope of the minimum contract balances the worker’s protection and the necessary flexibility for incentive provision.
Current version: April 2025.
A principal contracts with an agent who can sequentially search over projects to generate a prize. The principal knows only one of the agent's available projects and evaluates a contract by its worst-case performance. We characterize the set of robustly optimal contracts, all of which involve a minimum debt level, i.e., the agent only receives payment if the prize exceeds a certain threshold. This debt requirement is essential to prevent the agent from terminating the search too early. Our characterization encompasses several commonly observed contract formats, including pure debt, debt-plus-equity, and tranches. We also study situations where each of these contracts emerges as the unique prediction. In contrast to much of the existing robust contracting literature, linear contracts are strictly sub-optimal because they dampen the agent's search incentive.
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