Approximations for the Distribution of Perpetuities with Small Discount RatesJ. Blanchet and P. W. Glynn submitted for publication. Perpetuities (i.e. random variables of the form $D = \int_0^\infty e^{-\Gamma(t-)}d\Gamma(t)$ play an important role in many application settings. We develop approximations for the distribution of $D$ when the "accumulated short rate process", $\Gamma$, is small. We provide: 1) Characterizations for the distribution of $D$ when $\Gamma$ and $\Lambda$ are driven by Markov processes; 2) General sufficient conditions under which weak convergence results can be derived for $D$, and 3) Edgeworth expansions for the distribution of $D$ in the iid case and the case in which $\Gamma$ is a Levy process and the interest rate is a function of an ergodic Markov process. |