I have a Fund $F_t$ made of a bond ($B_t$) combined with an equity ($S_t$). $$F_t=S_t + B_t$$The dynamics are : $ dB_t = r B_tdt$ and $dS_t=rS_tdt + \sigma S_tdW_t$ where $r$ and $\sigma$ are constant quantities. I would write the dynamics of the fund as follow $$dF_t=dS_t+dB_t=rF_tdt + \sigma S_tdW_t$$ Looking at the result I would say it's not a GBM. I was expecting some know dynamics
2026-03-25 03:20:24.1774408824
Does the dynamics of this Fund follow a GBM?
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