Suppliers under sample demanders

There are always slightly fewer clerks than customers.

So a price index is really a dual process, one handling negative price change and on handling positive. The supplier is strongly risk averse.   Net price is probability of negative price shock exceeds positive price shock. That number is fixed to the supplier. The variance difference between price money in and good out must be bound for double entry accounting.

Liquidity is the entropy matching point, the -iLog(i).  Cash optimally matched to goods by segmenting cash. Price is dollars/goods, the compression ratio. We compress dollars in to dollars out.  Dollars in will be -ilog(i). Price is in/out.

Liquidity should be price  * delta price, and is maximum after compression.

The standard is to treats customer arrive has gaussian arrivals. The new method it to treat customers arrivals as a binomial, to some known accuracy. They deliver dollars. prices out are delivered by a separate process. We are ignoring conditionals. Then there is N, the node on the Markov tree, the 1,y,z line.  We are assuming suppliers are gaussian arrivalls, centered. This is actually a condition reported for suppliers to rebalance.

This works well for bankers who follow price indices.    Compress, lossy, the money sequence to match N, and the supplier sees dollars in and dollars, a finite set. Divided down so the information in dollars in  is maximum, information entropy maximum.

The bean counter then just delivers the finite compressed list of prices as a histogram. Each element gives the price where dollars is at maximum entropy, and the histogram area is -iLog(i) for the price in.  The difference with Shannon is that we know  N.  So we calculate noise power needed to make the match. Hidden Markov model.

We are matching noise to signal at the exact point that meets Shannon-Nyquist, and getting  N. Then we have two sample sequences, and they have to match the y,z.   (1, 89, 233), this is about as accurate as we will get. 233 dollars in quanta and 89 dollars out quanta.   A rank eight encoder for prices.

The finite set of prices will count out the total number N f transactions with bound error.  It should be a rank set of uniform sequences. Arrival rates count out the sequence indices in order.