On Equivalent Martingale Measures on Lp-space

Abstract

We apply the no-arbitrage and no-free lunch definitions of Kreps (1981). Arbitrage
is a linear algebraic notion, while free lunch is a topological notion. The notion of free
lunch, unlike that of arbitrage, is somewhat ambiguous because it depends on a
topological choice that is often tacit, i.e. there is source of problem when we use the
topology in our work.
Our main point in this paper is that how the choice of a topology which the
space are free lunches. We consider a number of topological spaces depending on:
(1) not a free lunch. (does not converge).
(2) a free lunch (converge to a positive limit).
(3) not a free lunch (converge to a non-positive limit).