Consider a long forward contract with payoff (S_{T}-K) on a jump diffusion risky asset (left(S_{t} ight)_{t in

Consider a long forward contract with payoff \(S_{T}-K\) on a jump diffusion risky asset \(\left(S_{t}\right)_{t \in \mathbb{R}_{+}}\)given by

\[d S_{t}=\mu S_{t} d t+\sigma S_{t} d B_{t}+S_{t^{-}} d Y_{t} .\]

a) Show that the forward claim admits a unique arbitrage-free price to be computed in a market with risk-free rate \(r>0\).

b) Show that the forward claim admits an exact replicating portfolio strategy based on the two assets \(S_{t}\) and \(\mathrm{e}^{r t}\).

c) Recover portfolio strategy of Question (b) using the optimal portfolio strategy formula (21.20).