August 12, 2025
A holding is an amount, instrument, and owner: h = (a, i, o). The owner o holds amount a of intrument i. They have the rights and obligations associated with owning the intsrument.
A portfolio is a set of holdings. Since this is just math we can assume the portfolio consists of all current holdings in the world even though we don’t know what those are.
An exchange is when a buyer accepts what a seller offers at a given time t.. The buyer holding h = (a,i,o) is exchanged for the seller’s holding h' = (a',i',o') resulting in a new portfolio after the exchange has settled. The portfolio at time t \{\ldots,(a,i,0),\ldots(a',i',o'),\ldots\} becomes \{\ldots,(a',i',0),\ldots(a,i,o'),\ldots\} after settlement.