Success or failure of a firm under different financing policies: A dynamic stochastic model
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- 作者：Cifarelli ; Michele D. ; Masciandaro ; Donato ; Peccati ; Lorenzo ; Salsa ; Sandro ; Tagliani ; Aldo
- 关键词：Financing and ruin of a firm ; Stochastic growth models for a firm ; ODEs of hypergeometric type ; Numerical treatment of PDEs ; Laplace transforms and moments of the solution of an ODE
- 刊名：European Journal of Operational Research
- 出版年：2002
- 出版时间：February 1, 2002
- 年：2002
- 卷：136
- 期：3
- 页码：471-482
- 全文大小：138 K
文摘
The value of a firm evolves in time, according to a standard Ito's stochastic differential equation, and under different types of financial support. In particular both the cases of legal and illegal financing are considered. The ruin/success probabilities for the firm are evaluated in closed form via special functions in the various settings. Some functionals of the process, which are relevant from the viewpoint of the financiers, (via Kac's lemma) are shown to obey a PDE, which is studied both with analytic tools (second-order ODEs of hypergeometric type) and with numerical ones. The case of insufficient payments is analyzed via stochastic calculus and a new model for loan renegotiation is offered.