Speaker: Filippo Beretta
Title: The role of preferences in Sannikov’s model
Abstract: We study the contracting model originally introduced by [Y. Sannikov, A continuous-time version of the principal–agent problem, 2008], building on the rigorous analyses provided in recent studies by [D. Possamaï and N. Touzi, Is there a golden parachute in Sannikov’s principal-agent problem?, 2024], as well as [D. Possamaï and C. Rossato, Golden parachutes under the threat of accidents, 2025]. A principal hires an agent to perform a task and compensate him with running payments throughout the contract’s duration, which concludes at a random time, potentially with a lump-sum payment upon termination. Firstly, we present results general enough to tackle the most classical (risk-averse) utility functions as exponential, negative power and logarithmic utility. The power-utility framework proposed in the above-mentioned studies represents an intermediate scenario between two extreme regimes, termed Grows More than Power (GMP) and Grows Less than Power (GLP). In the former, the problem is degenerate whenever the principal is strictly more impatient than the agent, while in the latter degeneracy never occurs. Secondly, we discuss the case of a risk-neutral agent. This scenario, characterized by the explosive feature of the associated Hamiltonian, leads to a series of singular stochastic control problems. We provide a complete, explicit solution for this case, resulting in optimal contracts that differ substantially from those in the risk-averse framework. Notably, these contracts are characterized by a singular nature, with lump-sum payments at initiation (a ‘welcome bonus’) and the involvement of local times (a ‘recurring bonus’ once some objectives are reached) throughout. The economic implications of this scenario differ substantially from Sannikov’s original findings.