We examine the problem of a risk-neutral investor who has to choose among two alternative projects of different scales under output price uncertainty. We show that as soon as investment in the smaller scale project is sometimes optimal, the optimal investment strategy is not a trigger strategy and the optimal investment region is dichotomous. Whenever the investor has the opportunity to switch from the smaller scale to the larger scale project, the dichotomy of the investment region can persist even when uncertainty becomes large.

We develop a dynamic model of a firm facing agency costs of free cash flow and external financing costs, and derive an explicit solution for the firm's optimal balance sheet dynamics. Financial frictions affect issuance and dividend policies, the value of cash holdings, and the dynamics of stock prices. The model predicts that the marginal value of cash varies negatively with the stock price, and positively with the volatility of the stock price. This yields novel insights on the asymmetric volatility phenomenon, on risk management policies, and on how business cycles and agency costs affect the volatility of stock returns.

* We are grateful to Bruno Biais, Nicole El Karouni, Christian Gollier and Damien Lamberton for thoughtful discussions and suggestions. We would also like to thank seminar participants at ESC Toulouse, Institut Henri Poincaré and Séminaire Bachelier for their comments. Financial support from STICERD is gratefully acknowledged by the second author. We remain, of course, solely responsible for the content of this paper. AbstractWe study the decision of when to invest in an indivisible project whose value is perfectly observable but driven by a parameter that is unknown to the decision maker ex ante. This problem is equivalent to an optimal stopping problem for a bivariate Markov process. Using filtering and martingale techniques, we show that the optimal investment region is characterised by a continuous and non-decreasing boundary in the value/belief state space. This generates path-dependency in the optimal investment strategy. We further show that the decision maker always benefits from an uncertain drift relative to an 'average' drift situation. However, a local study of the investment boundary reveals that the value of the option to invest is not globally increasing with respect to the volatility of the value process.

The ongoing reform of the Basel Accord relies on three "pillars": a new capital adequacy requirement, supervisory review and market discipline. This article develops a simple continuous-time model of commercial banks' behavior where the articulation between these three instruments can be analyzed. We study the conditions under which market discipline can reduce the minimum capital requirements needed to prevent moral hazard. We also discuss regulatory forbearance issues.

We study a duopoly model of investment, in which each player learns about the quality of a common value project by observing some public background information, and possibly the experience of his rival. Investment costs are private information, and the background signal takes the form of a Poisson process conditional on the quality of the project being low. The resulting attrition game has a unique, symmetric equilibrium, which depends on initial public beliefs. We determine the impact of changes in the cost and signal distributions on investment timing, and how equilibrium is affected when a first-mover advantage is introduced.