Unlike other industries in which intellectual property is patentable, the
financial industry relies on trade secrecy to protect its business processes
and methods, which can obscure critical financial risk exposures from
regulators and the public. We develop methods for sharing and aggregating such
risk exposures that protect the privacy of all parties involved and without the
need for a trusted third party.
The quantitative aspirations of economists and financial analysts have for
many years been based on the belief that it should be possible to build models
of economic systems - and financial markets in particular - that are as
predictive as those in physics. While this perspective has led to a number of
important breakthroughs in economics, "physics envy" has also created a false
sense of mathematical precision in some cases. We speculate on the origins of
physics envy, and then describe an alternate perspective of economic behavior
based on a new taxonomy of uncertainty.
We propose to study market efficiency from a computational viewpoint.
Borrowing from theoretical computer science, we define a market to be
\emph{efficient with respect to resources $S$} (e.g., time, memory) if no
strategy using resources $S$ can make a profit. As a first step, we consider
memory-$m$ strategies whose action at time $t$ depends only on the $m$ previous
observations at times $t-m,...,t-1$. We introduce and study a simple model of
market evolution, where strategies impact the market by their decision to buy
or sell.