Hu, K., Ren, Z., & Yang, J. (2023). Principal-agent problem with multiple principals. STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES, 95(5), 878–905. https://doi.org/10.1080/17442508.2022.2125808
E105 - Institut für Stochastik und Wirtschaftsmathematik
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Journal:
STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES
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ISSN:
1744-2508
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Date (published):
2023
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Number of Pages:
28
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Publisher:
TAYLOR & FRANCIS LTD
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Peer reviewed:
Yes
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Keywords:
backward SDE; contract theory; mean field games; Moral hazard; optimal switching; propagation of chaos
en
Abstract:
We consider a moral hazard problem with multiple principals in a continuous-time model. The agent can only work exclusively for one principal at a given time, so faces an optimal switching problem. Using a randomized formulation and techniques from the theory of backward SDEs, we manage to represent the agent's value function and his optimal effort by an Itô process. This representation further helps to solve the principals' problem in case we have infinite number of principals in the sense of mean field game. Finally, to justify the mean field formulation, we develop the so-called backward propagation of chaos, which may carry independent interest itself.