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Dynamic programming approach to principal–agent problems

Cvitanić, Jakša and Possamaï, Dylan and Touzi, Nizar (2018) Dynamic programming approach to principal–agent problems. Finance and Stochastics, 22 (1). pp. 1-37. ISSN 0949-2984. http://resolver.caltech.edu/CaltechAUTHORS:20171027-093026885

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Abstract

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, in which case the agent’s optimal effort is straightforward to find. We then show that the optimization over this restricted family of contracts represents no loss of generality. As a consequence, we have reduced a non-zero-sum stochastic differential game to a stochastic control problem which may be addressed by 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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/s00780-017-0344-4DOIArticle
https://link.springer.com/article/10.1007%2Fs00780-017-0344-4PublisherArticle
http://rdcu.be/D37fPublisherFree ReadCube access
https://arxiv.org/abs/1510.07111arXivDiscussion Paper
ORCID:
AuthorORCID
Cvitanić, Jakša0000-0001-6651-3552
Additional Information:© 2017 Springer-Verlag GmbH Germany. Received: 19 April 2016; Accepted: 27 March 2017; First Online: 27 October 2017.
Subject Keywords:Stochastic control of non-Markov systems; Hamilton–Jacobi–Bellman equations; Second order backward SDEs; Principal–agent problem; Contract theory
Classification Code:MSC: 91B40; 93E20. JEL: C61; C73; D82; J33; M52
Record Number:CaltechAUTHORS:20171027-093026885
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20171027-093026885
Official Citation:Cvitanić, J., Possamaï, D. & Touzi, N. Finance Stoch (2018) 22: 1. https://doi.org/10.1007/s00780-017-0344-4
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:82728
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:27 Oct 2017 16:40
Last Modified:04 Jan 2018 18:44

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