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04-11-2020 | Issue 2/2021

Mathematics and Financial Economics 2/2021

Scale effects in dynamic contracting

Journal:
Mathematics and Financial Economics > Issue 2/2021
Authors:
Shirley Bromberg-Silverstein, Santiago Moreno-Bromberg, Guillaume Roger
Important notes
We thank Andrea Barth, Cosimo Munari, Oleg Reichmann, Jean-Charles Rochet, Mario Šikić and Quynh Anh Vo for their helpful comments and suggestions, as well as participants at the 2015 Stanford Institute for Theoretical Economics (Segment IV) for stimulating discussion and seminar participants at Berkeley Haas, Melbourne, Monash, Stanford GSB, Sydney, UNSW, USC, UTS, UZH, the FIRN Corporate Finance conference and the FIRN Financial Stability conference. The research leading to these results has received funding from the ERC (Grant Agreement 249415-RMAC) from NCCR FinRisk (project “Banking and Regulation”) and from the Swiss Finance Institute (project “Systemic Risk and Dynamic Contract Theory”), and it is gratefully acknowledged.

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Abstract

We study a continuous-time contracting problem in which project scale plays a role. The agent may speculate to enhance the drift of a cash-flow process; doing so exposes the principal to large, infrequent losses. The optimal contract includes scale as an instrument: downsizing along the equilibrium path is necessary to preserve incentive compatibility. We characterize the optimal contract, and specifically the downsizing process, and prove there is an optimal liquidation scale that is reached in finite time. We also analyze some finer properties of the state variables of the contract and the resulting value function of the principal. The optimal contract is implemented using standard financial securities plus debt covenants; holding equity is essential to curb risk taking. Conflicts emerge between classes of security holders and explain phenomena like priority of claims at liquidation.

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