Kelly with a fat left tail

A short-option strategy returns, per unit of capital staked, $+5\%$ with probability 0.85, $-10\%$ with probability 0.13 and $-60\%$ with probability 0.02. (a) Compute $\mu_1,\mu_2,\mu_3$, the Gaussian Kelly $\mu/\sigma^2$, $\mu_1/\mu_2$ and $1/L$. (b) Find the exact Kelly fraction numerically and the growth rate per trade at $f^*$ and at $f^*/2$. (c) What happens to a trader who bets the Gaussian Kelly fraction? Relate to Proposition 9.11.