Generalized integrands and bond portfolios: Pitfalls and counter examples

We construct Zero-Coupon Bond markets driven by a cylindrical Brownian motion in which the notion of generalized portfolio has important flaws: There exist bounded smooth random variables with generalized hedging portfolios for which the price of their risky part is $+\mathrm{\infty }$ at each time. For these generalized portfolios, sequences of the prices of the risky part of approximating portfolios can be made to converges to any given extended real number in $[-\mathrm{\infty },\mathrm{\infty }]\mathrm{.}$