Bond Market Completeness and Attainable Contingent Claims
| dc.creator | Taflin, Erik | |
| dc.date | 2004-02-23 | |
| dc.date | 2005-03-03 | |
| dc.date.accessioned | 2026-07-07T09:40:31Z | |
| dc.date.available | 2026-07-07T09:40:31Z | |
| dc.description | A general class, introduced in [Ekeland et al. 2003], of continuous time bond markets driven by a standard cylindrical Brownian motion $\wienerq{}{}$ in $\ell^{2},$ is considered. We prove that there always exist non-hedgeable random variables in the space $\derprod{}{0}=\cap_{p \geq 1}L^{p}$ and that $\derprod{}{0}$ has a dense subset of attainable elements, if the volatility operator is non-degenerated a.e. Such results were proved in [Björk et al. 1997] in the case of a bond market driven by finite dimensional B.m. and marked point processes. We define certain smaller spaces $\derprod{}{s},$ $s>0$ of European contingent claims, by requiring that the integrand in the martingale representation, with respect to $\wienerq{}{}$, takes values in weighted $\ell^{2}$ spaces $\ell^{s,2},$ with a power weight of degree $s.$ For all $s > 0,$ the space $\derprod{}{s}$ is dense in $\derprod{}{0}$ and is independent of the particular bond price and volatility operator processes. A simple condition in terms of $\ell^{s,2}$ norms is given on the volatility operator processes, which implies if satisfied, that every element in $\derprod{}{s}$ is attainable. In this context a related problem of optimal portfolios of zero coupon bonds is solved for general utility functions and volatility operator processes, provided that the $\ell^{2}$-valued market price of risk process has certain Malliavin differentiability properties. | |
| dc.description | 27 pages, Revised version to be published in Finance and Stochastics | |
| dc.identifier | https://arxiv.org/abs/math/0402364 | |
| dc.identifier | http://arxiv.org/abs/math/0402364 | |
| dc.identifier | Finance and Stochastics Vol 9, 429--452 (2005) | |
| dc.identifier | doi:10.1007/s00780-005-0156-9 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/161509 | |
| dc.subject | Optimization and Control | |
| dc.subject | 91B28, 49J55, 60H07, 90C46, 46E35 | |
| dc.title | Bond Market Completeness and Attainable Contingent Claims | |
| dc.type | text |