An agent has wealth $X(t)$ at time $t$ and invests an amount $\Delta(t)$ of money into a stock $S(t)$ given by $$ dS(t) = \mu S(t)\, dt + \sigma S(t) \, dB(t). $$ In other words, the wealth process has representation $X(t) = (\Delta/S \bullet S)(t)$.
I don't understand why $X(t) = (\Delta/S \bullet S)(t)$. For me, it would be more intuitive to have $X(t) = (\Delta \bullet S)(t)$. Here $\bullet$ denotes the stochastic integral.