Bond portfolios

A portfolio of $m$ $T_i$-bonds ($i=1,\dots,m$) shall have price $\pi_t = \sum_i w_i\, P_t(T_i-t) =: \sum_i p_t^i = (1,\dots,1)\, p_t$, i.e. the value of the position in the $T_i$-bond at time $t$ is $p_t^i$. The price process satisfies

$$\mathrm{d}\pi_t = p_t^\prime\,U\left(\lambda(\xi_t)\mathrm{d}t - \Sigma\mathrm{d}W\right) + \pi_t\,r_t\,\mathrm{d}t \quad ,$$ (27)

where $U\in \mathbb{R}^{m \times n}$, $U=(u(T_1-t),\dots,u(T_m-t))^\prime$ .