Overview
An account balance model seeks to model 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 affected 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 receives 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 series 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.
If you willing to specify a long term growth rate, a Brownian Bridge may be an effective model of account balances that incorporates mean reversion.