On the portfolio strategy with the Meixner-Exponential distributional relationship

Abstract

The Meixner process as a special type of the Levy process is related to the Meixner-Pollaczek polynomial by a Martingale relation. Since discovered, the Meixner process has been applied to financial data to show that the Normal distribution is a very poor model to fit log-returns of financial assets like stocks and indices.

In this paper, we derived a distribution which is related to Meixner and Exponential distribution. We call this distributional relationship ‘the Meixner-Exponential distribution’ and fit it to financial data to show how good it fits. Furthermore, we apply the distribution to determine the expected value (wealth) of an investor whose initial wealth is  and whose returns is Rτ.