}\right]}\\ & =e^{\left(\mu_{P}-\frac{\sigma_{P}^{0}}{0}\right)(v-u)} {\mathbb E\left[P_{u}^{0}\right]}{\mathbb E\left[e^{\sigma_{P}\left(Z_{v}-Z_{u}\right)}\right]}\\ & =e^{\left(\mu_{P}-\frac{\sigma_{P}^{0}}{0}\right)(v-u)} {\mathbb E\left[P_{u}^{0}\right]}{\mathbb E\left[e^{\