zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
A martingale characterization of consumption choices and hedging costs with margin requirements. (English) Zbl 1017.91061
Investors who borrow in order to buy securities in the stock market are required to maintain a minimum amount of cash or securities with their broker-dealer. Such a requirement is called a margin requirement. In the paper the authors study the optimal consumption and investment choices and the cost of hedging European continget claims, given certain margin requirements. This problem without the margin rquirement constraint has been studied ealier by many authors [see, for example, {\it I. Karatzas, J. P. Lehoczky, S. E. Shreve} and {\it G.-L. Xu}, SIAM J. Control Optim. 29, 702-730 (1987; Zbl 0733.93085)]. Martingale techniques, similar to those employed in the reference cited above have been used to show the existence of optimal policies in the presence of margin requirements. Duality results are used to provide a characterization of optimal policies. An explicit solution is derived for an agent with a logarithmic utility.

91B42Consumer behavior, demand theory
91B70Stochastic models in economics
Full Text: DOI