Generalized integrands and bond portfolios: Pitfalls and counter examples

Details Generalized integrands and bond portfolios: Pitfalls and counter examples Generalized integrands and bond portfolios: Pitfalls and counter examples

2009-09-12

arxiv.org/abs/0909.2341v2

Annals of Applied Probability 2011, Vol. 21, No. 1, 266-282

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/10-AAP694 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/10-AAP694

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 $+\infty$ 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 $[-\infty,\infty].$

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