Abstract
Chapter 5 presents joint results of E.M. Stein and the author concerning the asymptotic behavior of mixing distribution densities associated with geometric Brownian motions, Ornstein-Uhlenbeck processes, and CIR-processes. Sharp asymptotic formulas with relative error estimates are established for these densities, using various combinations of techniques and tools. The proofs employ a Tauberian theorem for the two-sided Laplace transform, the theory of hypergeometric functions, and some methods from complex analysis. Dufresne’s recurrence formula, which allows one to navigate between the Hull-White models with different values of the model parameters, is also covered in Chap. 5.
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