We propose a model of dynamic investment, financing, and risk management for financially constrained firms. The model highlights the central importance of the endogenous marginal value of liquidity (cash and credit line) for corporate decisions. Our three main results are: (1) investment depends on the ratio of marginal q to the marginal value of liquidity, and the relation between investment and marginal q changes with the marginal source of funding; (2) optimal external financing and payout are characterized by an endogenous double-barrier policy for the firm's cashcapital ratio; and (3) liquidity management and derivatives hedging are complementary risk management tools.WHEN FIRMS FACE EXTERNAL financing costs, they must deal with complex and closely intertwined investment, financing, and risk management decisions. How to formalize the interconnections among these margins in a dynamic setting and how to translate the theory into day-to-day risk management and real investment policies remains largely to be determined. Questions such as how corporations should manage their cash holdings, which risks they should hedge and by how much, or the extent to which holding cash is a substitute for financial hedging are not well understood.Our goal in this article is to propose the first elements of a tractable dynamic corporate risk management framework-as illustrated in Figure 1-in which cash inventory, corporate investment, external financing, payout, and dynamic hedging policies are characterized simultaneously for a "financially constrained" firm. We emphasize that risk management is not just about financial hedging; instead, it is tightly connected to liquidity management via * Bolton is at Columbia University, NBER, and CEPR. Chen is at MIT Sloan School of Management and NBER. Wang is at Columbia University, NBER, and Shanghai University of Finance & Economics. We are grateful to Andrew Abel, Peter DeMarzo, Janice Eberly, Andrea Eisfeldt, Mike Faulkender, Michael Fishman, Xavier Gabaix, John Graham, Dirk Hackbarth, Cam Harvey, Christopher Hennessy, Pete Kyle, Yelena Larkin, Robert McDonald, Stewart Myers, Marco Pagano, Gordon Phillips, Robert Pindyck, Adriano Rampini, David Scharfstein, Jiang Wang, Toni Whited, two anonymous referees, and seminar participants at Boston College, Boston University, Columbia Business School, Duke, MIT Sloan, NYU Stern and NYU Economics, University of California at Berkeley, Yale, Maryland, Northwestern, Princeton, Lancaster, Virginia, IMF, Hong Kong University of Science and Technology Finance Symposium, Arizona State University, American Finance Association Meeting, the Caesarea Center 6th Annual Academic Conference, European Summer Symposium on Financial Markets, and Foundation for the Advancement of Research in Financial Economics for their comments. daily operations. By bringing these different aspects of risk management into a unified framework, we show how they interact with and complement each other.The baseline model we propose introduces only the essential building b...

Firms face uncertain financing conditions, which can be quite severe as exemplified by the recent financial crisis. We capture the firm's precautionary cash hoarding and market timing motives in a tractable model of dynamic corporate financial management when external financing conditions are stochastic. Firms value financial slack and build cash reserves to mitigate financial constraints. The finitely-lived favorable financing condition induces them to rationally time the equity market. This market timing motive can cause investment to be decreasing (and the marginal value of cash to be increasing) in financial slack, and can lead a financially constrained firm to gamble. Quantitatively, we find that firms' optimal responses to the threat of a financial crisis can significantly smooth out the impact of financing shocks on investments, marginal values of cash, and the risk premium over time. Thus, a firm may still appear unconstrained based on its relatively smooth investment over time despite significant underinvestment. This smoothing effect can be used to disentangle financing shocks from productivity shocks empirically. * We are grateful to Viral Acharya,

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We intend to show the potential of the numerical simulation of atmospheric turbulence to help find optimal sites for astronomical observation. We present results obtained with an atmospheric model, in which a representation of turbulence has been included. The model simulates the atmospheric flow over any given area, including the gross characteristics of the turbulence, from which maps of the astronomical seeing can be retrieved. A validation of the approach is obtained with actual measurements of the seeing, taken during field campaigns on two different sites. We find a good correlation in time between the observed and simulated values of the seeing, and we argue that this result can be extrapolated to space correlations.