We obtain the distribution of the maximal average in a sequence of independent identically distributed exponential random variables. Surprisingly enough, it turns out that the inverse distribution admits a simple closed form. An application to ruin probability in a risk-theoretic model is also given.
"On sequential maxima of exponential sample means, with an application to ruin probability." Electron. Commun. Probab. 24 1 - 7, 2019. https://doi.org/10.1214/19-ECP273