Explicit solutions to some single-period investment problems for risky log-stable stocks

Abstract

Numerical approximations are presented for the expected utility of wealth over a single time period for a small investor who proportions her or his available capital between a risk-free asset and a risky stock. The stock price is assumed to be a log-stable random variable. The utility functional is logarithmic or isoeleastic ( y a q , q < 0). Analytic results are presented for special choices of model parameters, and for large and small time periods.