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If

$${\rm Cov}[dW_t,dB_t]=\rho dt$$

then what is

$$\mathbb{E} \left[\int_0^t\sigma_{1s}dW_s \int_0^t\sigma_{2s}dB_s\right]$$

where $\sigma_{1s}$ and $\sigma_{2s}$ are two deterministic functions of $t$?

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