Account Balances

Overview

An account balance model seeks to mdoel the level of balances over time. It typically does not include any modeling of openings or closures.

Deterministic Balances

• Constant - one assumption is that the balance is constant or at lease relatively so. This may be justified if the total amount of deposits appears to be more affeccted by account openings and closing rather than by balances changing. In such a case, it may be more fruitful to focus on modeling openings and closings and to just assume a constant balance.
• Sawtooth - Some accounts, in particular accounts that are owned by a working individual, may show periodic deposits at the time the individual recieves their paycheck, and then a drawdown that occurs over the period until the next paydate.

The sawtooth function demonstrates account balances of a working individual.

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Balance as a Time Series

One possible method of modeling account balances is to assume that balances are a normal time series. One standard time seris is the Geometric Brownian Motion

For some models, the process needs to be constrained so that the balance is not allowed to grow to infinity. Typically, this involves some sort of Mean Reversion.