let's consider a stochastic volatility model for the stock price under the objective probability measure $P$ of the form
\begin{equation} \label{eq:system_loc_stoch_vol}
\begin{cases}
dS_t=\mu S_t dt+ F(Y_t) S_tdW_t \\
S_0=s_0 >0\\
dY_t= (m-Y_t )dt+ \nu dB_t \\
Y_0=y_0 \in \mathbb{R}
\end{cases}
\end{equation} This leads to an incomplete market.
In fact by Girsanov theorem we can build a family of risk neutral measures $\{Q^\gamma\}_\gamma$ for any bounded $\gamma$.
In this way under $Q^\gamma$ we have that the process $e^{-rt}S_t$ is an $\mathcal{F}_t$-martingale where $\mathcal{F}_t$ is the filtration generated by $(W_t,B_t)$.
Then $Q^\gamma$ is a family of risk neutral meausures and by the second fundamental theorem of asset pricing this is an incomplete market.
Instead from the first fundamental theorem of asset pricing we have that there is no arbitrage opportunity (or better the NFLVR holds).
Now take a $T$-claim $\Psi=\Psi(S_T)$. My question is: why the pricing formula for $\Psi$ is the following? $$V_t=\mathbb{E}^{Q^\gamma}[e^{-r(T-t)}\Psi(S_T)|\mathcal{F}_t]$$ How can we show it?
In a complete market the formula is correct by a replicating argument, but in an incomplete market why is it correct?
Thanks for your help.