Optimal stopping contract for Public Private Partnerships under moral hazard

Abstract

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.

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

“…2 Exceptions are the recent work by Hajjej, Hillairet, and Mnif [29], where the agent is risk-averse and more impatient than the principal. However, they do not obtain clear results saying that the hypotheses of their verification result [29,Theorem 4.3] can be verified in practice, as well as the work of Lin, Ren, Touzi, and Yang [41], but there the emphasis is more on obtaining general methods to attack infinite horizon moral hazard problems.…”

“…More precisely, when the principal is more impatient, but not too much (the actual bound depends on the level of risk-aversion of the agent), the solution exhibits no fundamental 1 Other early continuous-time contract theory models were proposed by Adrian and Westerfield [1], Biais, Mariotti, Plantin, and Rochet [4], Biais, Mariotti, Rochet, and Villeneuve [5], Biais, Mariotti, and Rochet [6], Capponi and Frei [9], DeMarzo and Sannikov [21], DeMarzo, Fishman, He, and Wang [22], Fong [26], He [30], Hoffmann and Pfeil [33], Ju and Wan [35], Keiber [37], Leung [39], Mirrlees and Raimondo [42], Myerson [45], Ou-Yang [46], Pagès [47], Pagès and Possamaï [48], Piskorski and Tchistyi [50], Piskorski and Westerfield [51], Sannikov [53], Schroder, Sinha, and Levental [58], Van Long and Sorger [68], Westerfield [69], Zhang [73], Zhou [74], or Zhu [75]. 2 Exceptions are the recent work by Hajjej, Hillairet, and Mnif [29], where the agent is risk-averse and more impatient than the principal. However, they do not obtain clear results saying that the hypotheses of their verification result [29,Theorem 4.3] can be verified in practice, as well as the work of Lin, Ren, Touzi, and Yang [41], but there the emphasis is more on obtaining general methods to attack infinite horizon moral hazard problems.…”