  This paper analyzes the robust long-term growth rate of expected utility and
expected return from holding a leveraged exchange-traded fund (LETF). When the
Markovian model parameters in the reference asset are uncertain, the robust
long-term growth rate is derived by analyzing the worst-case parameters among
an uncertainty set. We compute the growth rate and describe the optimal
leverage ratio maximizing the robust long-term growth rate. To achieve this,
the worst-case parameters are analyzed by the comparison principle, and the
growth rate of the worst-case is computed using the martingale extraction
method. The robust long-term growth rates are obtained explicitly under a
number of models for the reference asset, including the geometric Brownian
motion (GBM), Cox--Ingersoll--Ross (CIR), 3/2, and Heston and 3/2 stochastic
volatility models. Additionally, we demonstrate the impact of stochastic
interest rates, such as the Vasicek and inverse GARCH short rate models. This
paper is an extended work of \citet{Leung2017}.
