Pricing Asian options by PDEs. Show that the functions \(g(t, z)\) and \(h(t, y)\) are linked by the relation

\[g(t, z)=h\left(t, \frac{1-\mathrm{e}^{-(T-t) r}}{r T}+\mathrm{e}^{-(T-t) r} z\right), \quad 0 \leqslant t \leqslant T, \quad z>0\]

and that the PDE for \(h(t, y)\) can be derived from the PDE (1.33) for \(g(t, z)\) and the above relation.