Existence, Uniqueness, and Determinacy of Equilibria in Complete Security Markets with Infinite Dimensional Martingale Generator

Arbeitspapier

There is a strong evidence that most of financial variables are better described by a combination of difusion and jump processes. Considering such evidence, researchers have studied security market models with jumps, in particular, in the context of option pricing. In most of their models, jump magnitude is specified as a continuously distributed random variable at each jump time. Then, the dimensionality of martingale generator, which can be interpreted as the number of sources of uncertainty" in markets is infinite, and no finite set of securities can complete markets. In security market economy with infinite dimensional martingale generator, no equilibrium analysis has been conducted thus far. We assume approximately complete markets (Björk et al. [10] [11]) in which a continuum of bonds are traded and any contingent claim can be approximately replicated with an arbitrary precision. We introduce the notion of approximate security market equilibrium in which an agent is allowed to choose a consumption plan approximately supported with any prescribed precision. We prove that an approximate security market equilibrium in approximately complete markets can be identified with an Arrow-Debreu equilibrium. Then, we present sufficient conditions for the existence of equilibria in the case of stochastic differential utilities with Inada condition, and for the existence, uniqueness, and determinacy of equilibria in the case of additively separable utilities.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Discussion Paper ; No. 316

Classification and Topics

• Classification: Wirtschaft ; General Financial Markets: General (includes Measurement and Data) ; Exchange and Production Economies ; Existence and Stability Conditions of Equilibrium
• Subject: Wertpapierhandel ; Martingale ; Vollkommener Wettbewerb ; Allgemeines Gleichgewicht ; Gleichgewicht ; Theorie ; jump diffusion

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Kusuda, Koji
• Event: Veröffentlichung
• (who): University of Minnesota, Center for Economic Research
• (where): Minneapolis, MN
• (when): 2002

Further information

• Handle: http://hdl.handle.net/10419/23494
• Last update: 10.03.2025, 11:42 AM CET