In this paper we employ the concept of Value-at-Risk to model a kind of risk-averse behaviour of a firm which seeks to maximize profit à la Greenwald-Stiglitz [Greenwald, B.C., Stiglitz, J.E., 1993, Financial Market Imperfections and Business Cycles, Quarterly Journal of Economics 108 (1), 77-114]. It is shown that there exists a unique well-defined solution function which relates output to the firm's net worth, but that this function is not monotone. The latter is due to the fact that, whenever the VaR-constraint is not binding, the firm behaves in a risk-neutral fashion. It is also shown that in this context the Modigliani-Miller theorem applies only in the special case where there is no risk of bankruptcy.
Tulli, V., Weinrich, G., A firm's optimizing behaviour under a Value-at-Risk constraint, <<OPTIMIZATION>>, 2009; 58 (2): 213-226. [doi:10.1080/02331930701761573] [http://hdl.handle.net/10807/25666]
A firm's optimizing behaviour under a Value-at-Risk constraint
Tulli, Vanda;Weinrich, Gerd
2009
Abstract
In this paper we employ the concept of Value-at-Risk to model a kind of risk-averse behaviour of a firm which seeks to maximize profit à la Greenwald-Stiglitz [Greenwald, B.C., Stiglitz, J.E., 1993, Financial Market Imperfections and Business Cycles, Quarterly Journal of Economics 108 (1), 77-114]. It is shown that there exists a unique well-defined solution function which relates output to the firm's net worth, but that this function is not monotone. The latter is due to the fact that, whenever the VaR-constraint is not binding, the firm behaves in a risk-neutral fashion. It is also shown that in this context the Modigliani-Miller theorem applies only in the special case where there is no risk of bankruptcy.
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