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Watanabe, S. (1971) On Stochastic Differential Equation for Multidimensional Diffusion Processes with Boundary Condition. Journal of Mathematics of Kyoto University, 11, 169-180.

has been cited by the following article:

• TITLE: Credit Rating Modelled with Reflected Stochastic Differential Equations

  AUTHORS: Adeyemi Adewale Sonubi

  KEYWORDS: Brownian Local Time, Credit Rating, Cashflow, Default, Reflected Stochastic Differential Equation, Undefaultable

  JOURNAL NAME: Journal of Mathematical Finance, Vol.4 No.5, November 26, 2014

  ABSTRACT: This research paper is focused on the modelling of credit rating, using reduced form approach, in which intensity is defined endogenously based on the firm’s cashflow. It was modelled with reflected stochastic differential equation; this was adopted to evaluate the credit rating of a firm where the reflection function Ø(t) (i.e. Brownian local time) was used to detect default and measure time spent at default. Through this, the credit rating is estimated within [0,1]; where “0” is the state of default and “1” is interpreted as undefaultable within a time interval t≥[0, ∞) under consideration.