A Study of Dynamic Bilinear Stochastic Models with Applications to Economic Processes

A new result on the multiplicative and quotient properties of scalar bilinear Ito equations is presented. Employing this result and the well-known closed form solutions for the scalar cases, some Lie theory is used to obtain closed form solutions for a large class of multivariable bilinear Ito differential equations. The closed form solutions are employed to obtain discrete time representations for those systems that can be directly employed in computations. Some computational results for economic system examples are presented.