The Fundamental Theorem of Asset Pricingfor Unbounded Stochastic Processes (1998)

2008 ◽  
pp. 279-317
Author(s):  
Freddy Delbaen ◽  
Walter Schachermayer
Keyword(s):  
Stochastic Processes ◽  
Fundamental Theorem

The fundamental theorem of asset pricing for unbounded stochastic processes

1998 ◽  
Vol 312 (2) ◽  
pp. 215-250 ◽  
Author(s):  
F. Delbaen ◽  
W. Schachermayer
Keyword(s):  
Asset Pricing ◽  
Stochastic Processes ◽  
Fundamental Theorem

scholarly journals Toward a fundamental theorem of quantal measure theory

2012 ◽  
Vol 22 (5) ◽  
pp. 816-852 ◽  
Author(s):  
RAFAEL D. SORKIN
Keyword(s):  
Stochastic Processes ◽  
Path Integral ◽  
Fundamental Theorem ◽  
Measure Theory ◽  
Finite Lattice ◽  
Extension Problem ◽  
Integral Type ◽  
Causal Sets ◽  
Simple Event ◽  
Vector Valued

In this paper we address the extension problem for quantal measures of path-integral type, concentrating on two cases: sequential growth of causal sets and a particle moving on the finite lattice ℤn. In both cases, the dynamics can be coded into a vector-valued measure μ on Ω, the space of all histories. Initially, μ is just defined on special subsets of Ω called cylinder events, and we would like to extend it to a larger family of subsets (events) in analogy to the way this is done in the classical theory of stochastic processes. Since quantally μ is generally not of bounded variation, a new method is required. We propose a method that defines the measure of an event by means of a sequence of simpler events that in a suitable sense converges to the event whose measure we are seeking to define. To this end, we introduce canonical sequences approximating certain events, and we propose a measure-based criterion for the convergence of such sequences. Applying the method, we encounter a simple event whose measure is zero classically but non-zero quantally.

Stochastic Processes in Demography and Applications

1992 ◽  
Vol 46 (1) ◽  
pp. 172-173
Author(s):  
S. Mitra
Keyword(s):  
Stochastic Processes
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