  We consider a couple of integrodifferential PDEs arising from a stochastic
Markovian control problem subjected to initial-terminal conditions. These
equations correspond to the MFG system for a controlled jump-diffusion process.
We prove that for a specific choice of the control function the expectation of
the jump-diffusion process can be found explicitly. The study is an extension
of similar results known for the pure diffusion process. As an example, we show
how this can be applied to the problem of investors evaluating the trend of an
asset when choosing an optimal portfolio.
