In a previous job we built an advisor for banking and pensions using a mathematical optimiser solving over a model of the Danish tax rules. It would normally find enough tax savings to retire about a year earlier by finding the best savings strategies (e.g exploiting dynamic and temporal effects between taxation on spouses retiring at different times, using the house mortgage as a savings buffer to shift pension payouts to lower tax years etc). It was quite an eye opener.
I can give a few highlights: it had an exact model of a personal economy (savings, pensions, debt, houses, cars, boats and other assets) and the tax system and a projection engine capable of predicting the future cash flows for a person.
The projections were the basis for advising the client how to best manage their finances.
The advisor model could request an optimisation of how to best allocate the assets and liabilities over time from a mixed integer programming model built with GAMS. The latter optimisation model was not exact but it could generate close-to-optimal strategies for e.g. pension savings, buying houses and how to best spend the savings after retirement. The best strategies were then fed back into the exact model, evaluated and presented to the user.
It requires a pretty complex tax system to really generate a lot of value for the clients so its value was lower in the neighbouring countries that had separated their social systems more from the tax system.
It was developed by a Danish startup named Financys, which was acquired by Schantz (another Danish company) and this was later acquired by Keylane from the Netherlands. Unfortunately I don’t think there are any good, detailed information about the technology available any more.
