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- Title
Bond market completeness and attainable contingent claims.
- Authors
Taflin, Erik
- Abstract
A general class, introduced in [7], of continuous time bond markets driven by a standard cylindrical Brownian motioninis considered. We prove that there always exist non-hedgeable random variables in the spaceand thathas a dense subset of attainable elements, if the volatility operator is non-degenerate a.e. Such results were proved in [1] and [2] in the case of a bond market driven by finite dimensional Brownian motions and marked point processes. We define certain smaller spaces,s>0, of European contingent claims by requiring that the integrand in the martingale representation with respect totakes values in weightedspaces, with a power weight of degrees. For alls>0, the spaceis dense inand is independent of the particular bond price and volatility operator processes.A simple condition in terms ofnorms is given on the volatility operator processes, which implies if satisfied that every element inis 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-valued market price of risk process has certain Malliavin differentiability properties.
- Subjects
BOND market; WIENER processes; MARKET volatility; MARTINGALES (Mathematics); STOCHASTIC processes
- Publication
Finance & Stochastics, 2005, Vol 9, Issue 3, p429
- ISSN
0949-2984
- Publication type
Article
- DOI
10.1007/s00780-005-0156-9