Contract theory in continuous-time models
This book, split into eleven chapters, studies the area of continuous-time principal-agent models in economical theory and finance. The first two chapters present a quick introduction to this area and provide the fundamental problem formulations and examples in this domain, such as the principal-agent problem and single-period examples. The next two chapters consider the case of risk sharing under full information. In this simple case, for principal-agent problems where volatility is controlled, the authors show that the first best outcome is achievable by relatively simple contracts. A more general, nonlinear case is then studied for the general risk-sharing problem, including necessary and sufficient conditions for optimality. The next part of the book considers contracting under hidden action and the case of moral hazard. The authors introduce the mathematical theory underpinning the general moral hazard problem and study several variations, special cases and the general solvability of each model. The fourth part of the book moves to the more complex case of both a hidden action and hidden type, that is the case of moral hazard and adverse selection. Again the authors explain in detail the developed models and evaluate their assumptions, characteristics and solution properties. The last three chapters, covering roughly one third of this very interesting book, study the backward and forward-backward stochastic differential equations for the characterization of optimal contracts. The authors begin by introducing the backward stochastic differential equation theory for simple problems and determine the conditions for existence and uniqueness in each case. A detailed presentation of the stochastic maximum principle follows, including the link to stochastic control theory. The book concludes with an overview of the forward-backward stochastic differential equation systems which, in many cases and even in the linear case, do not have a solution.
optimal stochastic control, principal-agent model
scientific article; zbMATH DE number 6006266