Dynamic programming approach to principal-agent problems
Cvitanić, Jakša; Possamaï, Dylan; Touzi, Nizar (2018), Dynamic programming approach to principal-agent problems, Finance and Stochastics, 22, 1, p. 1–37. 10.1007/s00780-017-0344-4
TypeArticle accepté pour publication ou publié
Journal nameFinance and Stochastics
MetadataShow full item record
Division of the humanities and social sciences
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Centre de Mathématiques Appliquées - Ecole Polytechnique [CMAP]
Abstract (EN)We consider a general formulation of the Principal-Agent problem with a lump-sum payment on a finite horizon, providing a systematic method for solving such problems. Our approach is the following: we first find the contract that is optimal among those for which the agent's value process allows a dynamic programming representation, for which the agent's optimal effort is straightforward to find. We then show that the optimization over the restricted family of contracts represents no loss of generality. As a consequence, we have reduced this non-zero sum stochastic differential game to a stochastic control problem which may be addressed by the standard tools of control theory. Our proofs rely on the backward stochastic differential equations approach to non-Markovian stochastic control, and more specifically, on the recent extensions to the second order case.
Subjects / KeywordsStochastic control of non-Markov systems; Hamilton–Jacobi–Bellman equations; Second order backward SDEs; Principal–agent problem; Contract theory
JELM52 - Compensation and Compensation Methods and Their Effects
J33 - Compensation Packages; Payment Methods
D82 - Asymmetric and Private Information; Mechanism Design
C73 - Stochastic and Dynamic Games; Evolutionary Games; Repeated Games
C61 - Optimization Techniques; Programming Models; Dynamic Analysis
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