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## THE PRINCIPAL-AGENT PROBLEM; A STOCHASTIC MAXIMUM PRINCIPLE APPROACH

### Citations

427 |
Controlled Markov processes and viscosity solutions
- Fleming, Soner
- 1993
(Show Context)
Citation Context ...(·)| ≤ C(R) whenever |e| ≤ R for suitable C(R). Then e∗ is aMarkov control policy, i.e. a continuous function in all variables, being Lipschitz continuous on discs and of linear growth in x (see e.g. =-=[FS93]-=-, Theorem 11.1 p. 206). 14 BOUALEMDJEHICHE AND PETER HELGESSON Based on the information given by e∗ the principal wishes to minimize the cost JP by selecting a process s(·) respecting (3.4). The dynam... |

327 |
Aggregation and Linearity in the Provision of Intertemporal Incentives.
- Holmstrom, Milgrom
- 1987
(Show Context)
Citation Context ... assigned the agent will act as to maximize his/her own utility and not necessarily that of the principal. The first paper in which a continuous time version of the Principal-Agent problem appears is =-=[HM87]-=- by Holmström and Milgrom. They consider a model in which the agent takes action in continuous time over a finite period and gets rewarded by the principal at the end of this period. In particular, f... |

237 | Linear forward-backward stochastic differential equations
- Yong
- 1999
(Show Context)
Citation Context ...ons to forward-backward stochastic differential equations (from now on FBSDEs). The theory of FBSDEs is far from complete but well established in the stochastic analysis literature (see e.g. [Del02], =-=[MPY94]-=-, [MY99], [PW99], [Zha06], [Wu98]) and constrained optimal control of such equations has been studied for instance in Ji and Zhou [JZ06] and Ji and Wei [JW13]. The reason to approach the problem by me... |

135 |
A Continuous-Time Version of the Principal-Agent Problem,” Mimeo,
- Sannikov
- 2003
(Show Context)
Citation Context ...to resolve technical difficulties in discrete time models. The literature has therefore grown substantially, with contributions from many authors, including Cvitanić, Wan and Zhang [CWZ09], Sannikov =-=[San08]-=-, Westerfield [Wes06] and Williams [Wil13]. A thorough presentation of the field (with an emphasis on the mathematical aspects that arise) can be found in the book [CZ13] by Cvitanić and Zhang. In th... |

90 |
A general stochastic maximum principle for optimal control problems
- Peng
- 1990
(Show Context)
Citation Context ...ed diffusion coefficient σ(t, x, u), without changing the conclusion of Theorem 2.1. In the case of a non-convex control space the stochastic maximum principle with controlled diffusion was proven in =-=[Pen90]-=- and requires a solution (P,Q) of an additional adjoint BSDE. We choose to leave this most general form as reference in order to keep the presentation clear. As pointed out in Remark 2.2 it is a non-t... |

64 | On the existence and uniqueness of solutions to FBSDEs in a non-degenerate case. Stochastic Process - Delarue |

51 |
An introductory approach to duality in optimal stochastic control
- Bismut
- 1978
(Show Context)
Citation Context ...on and under hidden action (with the additional possibility to involve hidden savings of the agent). His idea is to attack the problem by applying the stochastic maximum principle suggested in Bismut =-=[Bis78]-=-. An explicit example is constructed as a fully dynamical analogue of the exponential utility model by Holmström and Milgrom, and is solved by using methods involving the dynamical programming princi... |

51 |
The first-order approach to the continuous-time principal agent problem with exponential utility.
- Schattler, Sung
- 1993
(Show Context)
Citation Context ...warded by the principal at the end of this period. In particular, for exponential utility functions they prove the optimal contract to be linear with respect to the output. In 1993 Schätter and Sung =-=[SS93]-=- generalized this seminal paper by suggesting a general mathematical framework based on the dynamic programming principle and martingale methods to characterize implementable contracts for a rich clas... |

50 | Fully coupled forward-backward stochastic differential equations and applications to optimal control
- Peng, Wu
- 1999
(Show Context)
Citation Context ...ckward stochastic differential equations (from now on FBSDEs). The theory of FBSDEs is far from complete but well established in the stochastic analysis literature (see e.g. [Del02], [MPY94], [MY99], =-=[PW99]-=-, [Zha06], [Wu98]) and constrained optimal control of such equations has been studied for instance in Ji and Zhou [JZ06] and Ji and Wei [JW13]. The reason to approach the problem by means of the stoch... |

36 |
Y.: Stochastic controls
- Yong, Zhou
- 1999
(Show Context)
Citation Context ...sixties (see e.g. [Kus65]) and, at least for strong solutions, the results seem to depend a lot upon the statement of the problem. In the weak sense, an account of existence results is to be found in =-=[YZ99]-=- (Theorem 5.3, p. 71). Remark 2.3. Restricting the space U to be convex allows for a controlled diffusion coefficient σ(t, x, u), without changing the conclusion of Theorem 2.1. In the case of a non-c... |

26 |
A maximum principle for SDEs of mean-field type
- Andersson, Djehiche
(Show Context)
Citation Context ...he subject (in pioneering papers by e.g. Bismut and Bensoussan in [Bis78] and [Ben82]) developed a lot and do by now apply to a wide range of problems more general than (S) (see for instance [Pen90], =-=[AD11]-=- [BDL11], [DTT14], to mention a few). For our purposes it will be necessary to have a refined version of Theorem 2.1, characterizing optimal controls in a FBSDE-dynamical setting under state constrain... |

20 |
Lectures on stochastic control, “Nonlinear filtering and stochastic control
- Bensoussan
- 1981
(Show Context)
Citation Context ...e in which U ⊆ R, equipped with the usual Euclidean metric. The stochastic maximum principle has since the early days of the subject (in pioneering papers by e.g. Bismut and Bensoussan in [Bis78] and =-=[Ben82]-=-) developed a lot and do by now apply to a wide range of problems more general than (S) (see for instance [Pen90], [AD11] [BDL11], [DTT14], to mention a few). For our purposes it will be necessary to ... |

18 |
A general stochastic maximum principle for sdes of mean-field type
- Buckdahn, Djehiche, et al.
(Show Context)
Citation Context ...ect (in pioneering papers by e.g. Bismut and Bensoussan in [Bis78] and [Ben82]) developed a lot and do by now apply to a wide range of problems more general than (S) (see for instance [Pen90], [AD11] =-=[BDL11]-=-, [DTT14], to mention a few). For our purposes it will be necessary to have a refined version of Theorem 2.1, characterizing optimal controls in a FBSDE-dynamical setting under state constraints. More... |

14 | A maximum principle for stochastic optimal control with terminal state constraints, and its applications
- Ji, Zhou
- 2006
(Show Context)
Citation Context ...ished in the stochastic analysis literature (see e.g. [Del02], [MPY94], [MY99], [PW99], [Zha06], [Wu98]) and constrained optimal control of such equations has been studied for instance in Ji and Zhou =-=[JZ06]-=- and Ji and Wei [JW13]. The reason to approach the problem by means of the stochastic maximum principle is twofold: Firstly, the method is versatile and does not rely on the dynamic programming princi... |

13 |
Contract Theory in Continuous-Time Models
- Cvitanić, Zhang
- 2012
(Show Context)
Citation Context ... and Zhang [CWZ09], Sannikov [San08], Westerfield [Wes06] and Williams [Wil13]. A thorough presentation of the field (with an emphasis on the mathematical aspects that arise) can be found in the book =-=[CZ13]-=- by Cvitanić and Zhang. In the present literature the paper closest to ours is [Wil13]. The aim of that article is to characterize optimal contracts as continuously paying cash-flows in a very genera... |

13 |
The maximum principle for fully coupled forwardbackward stochastic control system
- Shi, Wu
(Show Context)
Citation Context ...T]. To get a good maximum principle for (SC) we require some further regularity conditions ensuring solvability of (2.5). These conditions, denoted by (SC1)-(SC3) are stated below and can be found in =-=[SW06]-=-. All coefficient functions, and hence all x(·), y(·), z(·), are considered to be real valued. Let G ∈ R\{0} and introduce the following notation: v = xy z , A(t, v) = −G fGb Gσ (t, v)... |

9 | Optimal compensation with hidden action and lump-sum payment in a continuous-time model
- Cvitanić, Wan, et al.
- 2009
(Show Context)
Citation Context ...rs tractable ways to resolve technical difficulties in discrete time models. The literature has therefore grown substantially, with contributions from many authors, including Cvitanić, Wan and Zhang =-=[CWZ09]-=-, Sannikov [San08], Westerfield [Wes06] and Williams [Wil13]. A thorough presentation of the field (with an emphasis on the mathematical aspects that arise) can be found in the book [CZ13] by Cvitanic... |

8 |
Optimality Variational Principle for Controlled ForwardBackward Stochastic Differential Equations with Mixed InitialTerminal Conditions
- Yong
- 2010
(Show Context)
Citation Context ...imality. Following that scheme we end up with a coupled pair of stochastic optimization problems. The key required to set up the Principal-Agent problem in this way is (as also pointed out by Yong in =-=[Yon10]-=-) access to fundamental results concerning existence and uniqueness of solutions to forward-backward stochastic differential equations (from now on FBSDEs). The theory of FBSDEs is far from complete b... |

7 |
Optimal Stochastic Control,
- Kushner
- 1962
(Show Context)
Citation Context ...or optimality in (S). It does not claim the existence of such. Existence of stochastic optimal controls (both in the strong and the weak sense) has been a subject of study since the sixties (see e.g. =-=[Kus65]-=-) and, at least for strong solutions, the results seem to depend a lot upon the statement of the problem. In the weak sense, an account of existence results is to be found in [YZ99] (Theorem 5.3, p. 7... |

5 | Optimal contracts in continuous-time models
- Cvitanic, Wan, et al.
(Show Context)
Citation Context ...the scheme of solving the Hidden Contract model it becomes clear that many cases allow for Fx-adapted optimal cash-flows s(·). This is in line with present literature in Full Information-models (e.g. =-=[CWZ06]-=-) and motivates our approach. THE PRINCIPAL-AGENT PROBLEM 13 It is important to note that even though the principal cannot observe the agent’s effort, he/she can still offer the agent a contract by su... |

4 |
A maximum principle for fully coupled forward-backward stochastic control systems with terminal state constraints,”
- Ji, Wei
- 2013
(Show Context)
Citation Context ...c analysis literature (see e.g. [Del02], [MPY94], [MY99], [PW99], [Zha06], [Wu98]) and constrained optimal control of such equations has been studied for instance in Ji and Zhou [JZ06] and Ji and Wei =-=[JW13]-=-. The reason to approach the problem by means of the stochastic maximum principle is twofold: Firstly, the method is versatile and does not rely on the dynamic programming principle which opens up the... |

3 |
The wellposedness of FBSDEs, Discrete
- Zhang
(Show Context)
Citation Context ...tochastic differential equations (from now on FBSDEs). The theory of FBSDEs is far from complete but well established in the stochastic analysis literature (see e.g. [Del02], [MPY94], [MY99], [PW99], =-=[Zha06]-=-, [Wu98]) and constrained optimal control of such equations has been studied for instance in Ji and Zhou [JZ06] and Ji and Wei [JW13]. The reason to approach the problem by means of the stochastic max... |

2 |
Optimal control of probability density functions of stochastic processes
- Annunziato, Borzì
(Show Context)
Citation Context ...bject to the constraint JA(ϕ(·); s.) = ∫ T 0 ∫ R ( ϕ(t, z, s.)2 2 − s(t, z) ) µ(t, z)dzdt < W0. This problem, however, goes beyond the scope of our presentation and we leave it for a future study. In =-=[AB10]-=- and recently in [ABNT14] the authors explore the general possibility of the above approach to stochastic optimal control, thus formulating the problem in terms of optimal control of the Fokker-Planck... |

2 | A Stochastic Maximum Principle for Risk-Sensitive Mean-Field Type Control. Preprint: arXiv:1404.1441
- Djehiche, H, et al.
- 2014
(Show Context)
Citation Context ...ioneering papers by e.g. Bismut and Bensoussan in [Bis78] and [Ben82]) developed a lot and do by now apply to a wide range of problems more general than (S) (see for instance [Pen90], [AD11] [BDL11], =-=[DTT14]-=-, to mention a few). For our purposes it will be necessary to have a refined version of Theorem 2.1, characterizing optimal controls in a FBSDE-dynamical setting under state constraints. More precisel... |

2 |
On Dynamic Principal-Agent
- Williams
- 2013
(Show Context)
Citation Context ...ete time models. The literature has therefore grown substantially, with contributions from many authors, including Cvitanić, Wan and Zhang [CWZ09], Sannikov [San08], Westerfield [Wes06] and Williams =-=[Wil13]-=-. A thorough presentation of the field (with an emphasis on the mathematical aspects that arise) can be found in the book [CZ13] by Cvitanić and Zhang. In the present literature the paper closest to ... |

1 |
Tempone, On the connection between the Hamilton-Jacobi-Bellman and the Fokker-Planck control frameworks
- Annunziato, Borzi, et al.
(Show Context)
Citation Context ... JA(ϕ(·); s.) = ∫ T 0 ∫ R ( ϕ(t, z, s.)2 2 − s(t, z) ) µ(t, z)dzdt < W0. This problem, however, goes beyond the scope of our presentation and we leave it for a future study. In [AB10] and recently in =-=[ABNT14]-=- the authors explore the general possibility of the above approach to stochastic optimal control, thus formulating the problem in terms of optimal control of the Fokker-Planck equation. Their setting ... |

1 | Adapted solutions of forward-backward stochastic differential equations and their parameter dependence, Chinese Ann - Wu - 1998 |