Abstract
AbstractPerpetuities (i.e., random variables of the form play an important role in many application settings. We develop approximations for the distribution of when the “accumulated short rate process”, , is small. We provide: (1) characterizations for the distribution of when and are driven by Markov processes; (2) general sufficient conditions under which weak convergence results can be derived for , and (3) Edgeworth expansions for the distribution of in the iid case and the case in which is a Levy process and the interest rate is a function of an ergodic Markov process.
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