We have a regular self-financing portfolio $W_t$: $$dW_t = n_t dS_t + (W_t − n_t S_t) r dt$$ Where $W_t$ is total wealth, $n_t$ is amount of stock, $S_t$ is stock price, $r$ is the risk-free rate. And the strategy is to keep the stock exposure φ constant:

$φ = n_t S_t/W_t$

Currently I'm having trouble while trying to develop a formula for $n_t$, using $dS_t$ and $dt$.



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