Problem $3($Valuating the stock price of a company$)$

Suppose that our portfolio consists of the following $3$ financial instruments: $H_m$ shares of the index fund, $H_b$ shares of the risk$-$free government bond, and $H_o$ shares of the call option.

Market portfolio

$($an index fund, with the worth of $$\frac{100}{?}$ share$)$

$\backslash$table$[[,,\backslash$table$[[$worth of $1$ share of$],[$the index fund at the$],[$end of $1$ year$]]],[,\backslash$table$[[$Boom$],[$prob$.=0\mathrm{.}36$