Consider the price process \(\left(S_{t}ight)_{t \in[0, T]}\) given by

\[
\frac{d S_{t}}{S_{t}}=r d t+\sigma d B_{t}
\]

and a riskless asset valued \(A_{t}=A_{0} \mathrm{e}^{r t}, t \in[0, T]\), with \(r>0\). In this problem, \(\left(\eta_{t}, \xi_{t}ight)_{t \in[0, T]}\) denotes a portfolio strategy with value

\[
V_{t}=\eta_{t} A_{t}+\xi_{t} S_{t}, \quad 0 \leqslant t \leqslant T
\]

a) Compute the arbitrage-free price

\[
C\left(t, S_{t}ight)=\mathrm{e}^{-(T-t) r} \mathbb{E}^{*}\left[\left|S_{T}ight|^{2} \mid \mathcal{F}_{t}ight]
\]

at time \(t \in[0, T]\), of the power option with payoff \(C=\left|S_{T}ight|^{2}\).

b) Compute a self-financing hedging strategy \(\left(\eta_{t}, \xi_{t}ight)_{t \in[0, T]}\) hedging the claim payoff \(\left|S_{T}ight|^{2}\).