Valuation with noisy data and informative prices

Suppose everyone in the market for a particular asset has access to some very noisy information from which they can calculate the value of that asset. I am thinking of this information as private, though I believe that I really mean that each market participant evaluates primarily public information using their own algorithm for calculating the value from the shared data. These algorithms each have mean zero error, but with algorithm-specific varience in that error. Asset values change and valuation updating is costly. Market participants can buy or short-sell the asset as they believe it is over- or under-valued

Participants do not know what the algorithms of the other participants are. However they do have common access to the price history of the asset.

The above is intended to be a rough cut at a realistic description of how securities prices are determined.

Suppose I am a participant in this market. My intuition is that the market price conveys information, and that I probably want my asset valuation estimate to be some increasing function of my own valuation based on my private judgement and the market price, perhaps a weighted average. If I knew the variance in the errors of my past valuations, which I don't because the true valuation is not in the information set, I imagine I should weigh the market value more highly as my own valuation estimate is more uncertain. Now, here is my question: is there an optimal, or a good, or a not obviously stupid way of combining the price history data with my own asset valuation estimate to produce a revised and improved valuation.

My goal in doing this valuation is to decide whether to go long or short on the asset in a way that minimizes, or at least reduces, the likelihood that in doing one of these things I will lose money on the transaction. I assume other market participants are doing valuation with the same goal.



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