Exponential Family Techniques for the Lognormal Left Tail

Soren Asmussen, Jens Ledet Jensen, Leonardo Rojas-Nandayapa

Let $X$ be lognormal$(\mu ,{\sigma }^2)$ with density $f(x)$, let $\theta >0$ and define $L(\theta )=E{e}^{-\theta X}$. We study properties of the exponentially tilted density (Esscher transform) $f_θ(x) =e^{…