In the context of large financial markets we formulate the notion of no asymptotic free lunch
with vanishing risk (NAFLVR), under which we can prove a version of the fundamental …

Stochastic integrals are defined with respect to a collection P=(P i; i∈ I) of continuous
semimartingales, imposing no assumptions on the index set I and the subspace of RI where …

A wealth-process set is abstractly defined to consist of nonnegative càdlàg processes
containing a strictly positive semimartingale and satisfying an intuitive re-balancing property …

We present a surprisingly simple version of the fundamental theorem of asset pricing (FTAP)
for continuous time large financial markets with two filtrations in an L^p-setting for 1≦p<∞ …

We consider infinite-dimensional optimization problems motivated by the financial model
called Arbitrage Pricing Theory. Using probabilistic and functional analytic tools, we provide …

We introduce a theory of stochastic integration with respect to a family of semimartingales
depending on a continuous parameter, as a mathematical background to the theory of bond …

We study a large financial market where the discounted asset prices are modeled by
martingale random fields. This approach allows the treatment of both the cases of a market …

We consider a popular model of microeconomics with countably many assets: the Arbitrage
Pricing Model. We study the problem of optimal investment under an expected utility criterion …

This paper has two purposes. The first is to extend the notions of an n-dimensional
semimartingale and its stochastic integral to a piecewise semimartingale of stochastic …

We study the problem of expected utility maximization in a large market, ie, a market with
countably many traded assets. Assuming that agents have von Neumann–Morgenstern …