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)
Existence and uniqueness of multi-agent equilibrium in a stochastic, dynamic consumption/investment model. (English) Zbl 0707.90018
We consider an economy in which a set of agents own productive assets which provide commodity dividend streams, and the agents also receive individual commodity income streams, over a finite time horizon. The agents can buy and sell the commodity at a certain spot price and buy and sell their shares of the productive assets. The proceeds can be invested in financial assets whose prices are modelled as semimartingales. Each agent’s objective is to choose a commodity consumption process and to manage his portfolio so as to maximize the expected utility of his consumption, subject to havin nonnegative wealth at the terminal time. We derive the optimal agent consumption and investment decision processes when the prices of the productive assets and commodity spot prices are specified. We prove the existence and uniqueness of an “equilibrium” commodity spot price process and productive asset prices. When the agents solve their individual optimization problems using the equilibrium prices, all of the commodity is exactly consumed as it is received, all of the productive assets are exactly owned and the financial markets are in zero net supply.
Reviewer: I.Karatzas

91B62Growth models in economics
91B50General equilibrium theory in economics
91B28Finance etc. (MSC2000)
60H10Stochastic ordinary differential equations
60J25Continuous-time Markov processes on general state spaces
91B24Price theory and market structure
93E20Optimal stochastic control (systems)
Full Text: DOI