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 and look for conditions ensuring the existence of
optimal strategies. Previous results required a certain restrictive hypothesis
on the tails of asset return distributions. Using a different method, we manage
to remove this hypothesis, at the price of stronger assumptions on the moments
of asset returns.Comment: 12 pages, slightly revise
