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Assuming the limitations of this model, every transaction that has ever occurred in the world can be modeled by this. Limit orders, and more exotic variants, ultimately result in a transaction that is captured by this model. Over-the-counter trades are precisely modeled by this. At the end of the day transactions must be accounted for and open positions need to be marked. The real world is a messy place and it is not easy for math to keep up, but it can easily model the accounting aspects.

Given a set of transactions {χ = (*t*; *a*, *i*, *
c*; *a*', *i*', *c*')}, let

A(t;i,c;c') = Σ_{χ}{a_{χ}:t_{χ}=t,i_{χ}=i,c_{χ}=c,c'_{χ}=c'} + {a'_{χ}:t_{χ}=t,i'_{χ}=i,c_{χ}=c,c'_{χ}=c'}

This is the amount at time *t* that buyer *c* transacts in instrument
*i* with seller *c*'. The standard theory does not distinguish the selling counterparties so we can write

A(t,i,c) = Σ_{c'}A(t,i,c,c')

The standard theory also does not distinguish the buyer, so we can abbreviate this to
*A*(*t*, *i*); the amount you transact at time *t* in instrument
*i*.

Your account balance at time *t* in instrument *i* is

B(t,i) = Σ_{s≤t}A(s,i)

Last edited Jul 8, 2011 at 3:49 PM by keithalewis, version 22