  It is well-known that there are a number of relations between theoretical
finance theory and information theory. Some of these relations are exact and
some are approximate. In this paper we will explore some of these relations and
determine under which conditions the relations are exact. It turns out that
portfolio theory always leads to Bregman divergences. The Bregman divergence is
only proportional to information divergence in situations that are essentially
equal to the type of gambling studied by Kelly. This can be related an abstract
sufficiency condition.
