Drawdown control with gaps

Use the rule of Proposition 14.14 in discrete time: exposure $mC_{t}$ held over period $t+1$, return $R_{t+1} \ge -g$. (a) Prove that $C_{t+1} > 0$ for all $t$ if $mg < 1$, and give an example where $mg > 1$ breaches the floor. (b) With $d = 10\%$, $m = 5$, at a new equity high of ₹100 lakh, the stock gaps down 25% overnight. Compute the new drawdown. (c) What is the largest $m$ consistent with a worst plausible overnight gap of 15% on a single stock? What exposure does that allow at a new high?