Comparative Valuation Dynamics in Models with Financing Restrictions∗
Lars Peter Hansen
University of Chicago
University of Chicago
June 27, 2018
This type of equity-issuance constraint, sometimes called a “skin-in- the-game” constraint, can be derived from a primitive moral hazard problem.
Solution Method. In Appendix A.2, we apply a dynamic programming approach to solve agents’ optimization problems, which delivers a pair of Hamilton-Jacobi-Bellman (HJB) equations. Each is a 4-dimensional second-order nonlinear partial differential equation (PDE) for agents’ value functions. Next, in Appendix A.3, we use the market clearing conditions and constraints to solve for all equilibrium objects, in terms of the state variables and the value functions. By reinserting these equilibrium prices and dynamics in the HJB equations, the entire equilibrium fixed point problem boils down to solving a pair of PDEs for agents’ value functions. As a baseline numerical method, we implement an implicit finite difference scheme, which augments the PDE with an artificial time-derivative (“false transient”) in order to it- erate on the nonlinearities in the PDE system. More details on this procedure, as well as comparisons with an explicit scheme, are contained in Appendix B.
Risk-taking over the Life Cycle: Aggregate and Distributive Implications of Entrepreneurial Risk
Dejanir H. Silva Robert M. Townsend
UIUC ∗ MIT
Introducing idiosyncratic risk into the model opens the door to a potential moral hazard problem,
as idiosyncratic shocks are typically hard to monitor. We assume that aggregate shocks are public information, but idiosyncratic shocks are private information to the entrepreneur. This will limit the amount of idiosyncratic insurance an entrepreneur can contract. Entrepreneurs will be subject to a skin-in-the-game constraint and will be able to insure at most a fraction 0 ≤ φ ≤ 1 of idiosyncratic risk, where φ = 1 amounts to full insurance and φ = 0 financial autarky. In contrast, entrepreneurs are allowed to buy aggregate insurance freely.
The Lagrange multiplier on this skin-in-the-game constraint plays an important role in the entrepreneurs’ risk-taking decision. It turns out that the risk-taking decision of the entrepreneur depends only on the effective risk aversion, the level of idiosyncratic risk, and this multiplier, which we refer to as the shadow price of idiosyncratic insurance
Лет через двадцать-тридацать нобелевки просто валом посыпятся на все темы, по которым
я первым прошел. Потому что, ну “других” то тем, заслуживающих, их же просто фактически нет.
Да и филдсовских лауреатов по этим темам будет в достаточном количестве, математически проблемы
довольно сложны и вполне заслуживают усилий лучших из лучших математиков.