Prediction Markets for Classification
Mindika Premachandra
CS HDR MONITORINGDATE: 2012-10-29
TIME: 09:30:00 - 10:00:00
LOCATION: NICTA - 7 London Circuit
CONTACT: JavaScript must be enabled to display this email address.
ABSTRACT:
Assuming inhomogeneous utility participants in a fixed price sequential market setting, we ask the question of whether we can extract the participant beliefs (and possibly the underlying utility function) by observing their trades in the market, so that aggregation of beliefs may be done separately using more standard machine learning methods. We may have to assume non-strategic, myopic participants and generally where participants use their own belief (judgement) in determining the trade. Using the popular HARA utility class (u(m) = 1/(1-gamma)* (gamma(M + alpha m/gamma)^(1-gamma) - 1) with alpha > 0, which encompasses the quadratic, linear, CARA (negative exponential decay), CRRA (Iso-elastic) and log utilities), it can be shown that in the case of non-linear HARA utilities the participants utilities' can be extracted after observing two trades they make with the same beliefs. It follows that knowing their utility functions enables beliefs to be extracted in subsequent trades.
With regard to the properties of bounded wealth, decreasing demands, no debt and stationary only at belief used in the analysis of (Frongillo et al., 2012), it can be shown that gamma > 0 which includes CARA, CRRA and log utility satisfies the decreasing demands property while CRRA and log utilities also satisfy the no-debt constraint naturally. Another way to interpret the no-debt constraint may be that gamma.M/alpha in the utility represents an unused cash reserve which qualifies the entire non-linear HARA class with gamma >0 to be performing ex-post debt-free trades.
BIO:
