  Recently, several new pari-mutuel mechanisms have been introduced to organize
markets for contingent claims. Hanson introduced a market maker derived from
the logarithmic scoring rule, and later Chen and Pennock developed a cost
function formulation for the market maker. On the other hand, the SCPM model of
Peters et al. is based on ideas from a call auction setting using a convex
optimization model. In this work, we develop a unified framework that bridges
these seemingly unrelated models for centrally organizing contingent claim
markets. The framework, developed as a generalization of the SCPM, will support
many desirable properties such as proper scoring, truthful bidding (in a myopic
sense), efficient computation, and guarantees on worst case loss. In fact, our
unified framework will allow us to express various proper scoring rules,
existing or new, from classical utility functions in a convex optimization
problem representing the market organizer. Additionally, we utilize concepts
from duality to show that the market model is equivalent to a risk minimization
problem where a convex risk measure is employed. This will allow us to more
clearly understand the differences in the risk attitudes adopted by various
mechanisms, and particularly deepen our intuition about popular mechanisms like
Hanson's market-maker. In aggregate, we believe this work advances our
understanding of the objectives that the market organizer is optimizing in
popular pari-mutuel mechanisms by recasting them into one unified framework.
