Consider an underlying asset price process \(\left(S_{t}ight)_{t \in \mathbb{R}_{+}}\)under a risk-neutral measure \(\mathbb{P}^{*}\) with risk-free interest rate \(r\).

a) Does the European call option price \(C(K):=\mathrm{e}^{-r T} \mathbb{E}^{*}\left[\left(S_{T}-Kight)^{+}ight]\)increase or decrease with the strike price \(K\) ? Justify your answer.

b) Does the European put option price \(C(K):=\mathrm{e}^{-r T} \mathbb{E}^{*}\left[\left(K-S_{T}ight)^{+}ight]\)increase or decrease with the strike price \(K\) ? Justify your answer.