A two-dimensional control problem arising from dynamic contracting theory

Décamps, Jean‐Paul; Villeneuve, Stéphane

doi:10.1007/s00780-018-0376-4

Cited by 7 publications

(4 citation statements)

References 26 publications

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“…The book of Cvitanić and Zhang [19] focusing on the use of backward stochastic differential equations (BSDEs) is a case in point. So are the papers [60,20], and the more recent work of Cvitanić, Possamaï and Touzi [18] published in Finance and Stochastics. By highlighting clearly the real nature of Sannikov's trick, the latter became instrumental in the recent mathematical developments on the subject.…”

Section: Contract Theorymentioning

confidence: 99%

The influence of economic research on financial mathematics: Evidence from the last 25 years

Carmona

2021

Finance Stoch

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Section: Contract Theorymentioning

confidence: 99%

The influence of economic research on financial mathematics: Evidence from the last 25 years

Carmona

2021

Finance Stoch

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“…Nonetheless, existence of optimal contracts is not addressed there, and the results rely on the assumption that it is never optimal to retire the agent temporarily, while our approach actually proves that this is the case. We also would like to refer to the recent work of Décamps and Villeneuve [20], where the authors study a related, but different, contracting problem, and where again the heart of the analysis is technical clarity: this should be an additional illustration that actually proving rigorously results in this literature is a challenging task.…”

Section: Introductionmentioning

confidence: 99%

Is there a Golden Parachute in Sannikov's principal-agent problem?

Possamaï¹,

Touzi²

2020

Preprint

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This paper provides a complete review of the continuous-time optimal contracting problem introduced by Sannikov [54], in the extended context allowing for possibly different discount rates of both parties. The agent's problem is to seek for optimal effort, given the compensation scheme proposed by the principal over a random horizon. Then, given the optimal agent's response, the principal determines the best compensation scheme in terms of running payment, retirement, and lump-sum payment at retirement.A Golden Parachute is a situation where the agent ceases any effort at some positive stopping time, and receives a payment afterwards, possibly under the form of a lump sum payment, or of a continuous stream of payments. We show that a Golden Parachute only exists in certain specific circumstances. This is in contrast with the results claimed by Sannikov [54], where the only requirement is a positive agent's marginal cost of effort at zero. Namely, we show that there is no Golden Parachute if this parameter is too large. Similarly, in the context of a concave marginal utility, there is no Golden Parachute if the agent's utility function has a too negative curvature at zero.In the general case, we provide a rigorous analysis of this problem, and we prove that an agent with positive reservation utility is either never retired by the principal, or retired above some given threshold (as in Sannikov's solution). In particular, different discount factors induce naturally a face-lifted utility function, which allows to reduce the whole analysis to a setting similar to the equal-discount rates one. Finally, we also confirm that an agent with small reservation utility does have an informational rent, meaning that the principal optimally offers him a contract with strictly higher utility value.

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“…Anderson et al [1] studied the optimal replacement time (either for the sake of incentive provision, or for the sake of growth) of managers operating for a long-lived firm. Décamps and Villeneuve [10] studied the optimal strategic liquidation time, in a framework where the firm's profitability is impacted by the unobservable managerial effort of the agent. In this setting the principal's problem appears to be a 2-dimensional fully degenerated Markov control problem and the optimal contract that implements full effort is derived.…”

Section: Introductionmentioning

confidence: 99%

“…In this setting the principal's problem appears to be a 2-dimensional fully degenerated Markov control problem and the optimal contract that implements full effort is derived. Both papers [1] and [10] assume the agents and the principal to be risk neutral.…”

Section: Introductionmentioning

confidence: 99%

Optimal stopping contract for Public Private Partnerships under moral hazard

Hajjej¹,

Hillairet²

2019

Preprint

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This paper studies optimal Public Private Partnerships contract between a public entity and a consortium, in continuous-time and with a continuous payment, with the possibility for the public to stop the contract. The public ("she") pays a continuous rent to the consortium ("he"), while the latter gives a best response characterized by his effort. This effect impacts the drift of the social welfare, until a terminal date decided by the public when she stops the contract and gives compensation to the consortium. Usually, the public can not observe the effort done by the consortium, leading to a principal agent's problem with moral hazard. We solve this optimal stochastic control with optimal stopping problem in this context of moral hazard. The public value function is characterized by the solution of an associated Hamilton Jacobi Bellman Variational Inequality. The public value function and the optimal effort and rent processes are computed numerically by using the Howard algorithm. In particular, the impact of the social welfare's volatility on the optimal contract is studied.

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A two-dimensional control problem arising from dynamic contracting theory

Cited by 7 publications

References 26 publications

The influence of economic research on financial mathematics: Evidence from the last 25 years

The influence of economic research on financial mathematics: Evidence from the last 25 years

Is there a Golden Parachute in Sannikov's principal-agent problem?

Optimal stopping contract for Public Private Partnerships under moral hazard

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