August 29th, 2005, 9:24 pm
Since typically it is the logarithm that is modelled as a stochastic process, the power utility offers tractability: suppose that the utility is given by U_t = S_t^a and s_t = log(S_t) is a stoch process, say a random walk with S_0=1. Then we can write S_t = exp(s_t), and U_t = exp(a s_t), both having the same form. Since it is the MRS that we normally use, we can differentiate the utility, which will maintain its exponential form: M_t = U'_t/U'_0 = exp(a s_t)In addition, such a MRS is `equivalent' to Girsanov's theorem and the Esscher transform, providing a link between discrete and continuous time models.I don't think that exponential utility is that tractable, too many nested exponentials.Kyriakos