crescet pool

The traditional 'asset allocation' industry typically makes 'investor risk appetite' your problem, not theirs.  They then perform this outdated pre-MPT analysis of the kinds of asset your risk profile might need.  In reality, you need them all, in toto, and your risk appetite only drives the degree of leverage on that total portfolio.  Secondly, using some nineteenth century maths on annuities and perpetuities, they take your requirement of needing a fixed amount at a date in the future, run the formula, and work out what your monthly premium ought to be to achieve that future cashflow.  Note this too works only by eliminating all asset types and strategies except relatively safe loans/bonds, together with a hope that inflation doesn't destroy the real future value.  However, if you're willing to accept uncertainty in the primary return stream (which becomes increasingly OK  the longer your relevant time horizon is), then you can replace a safe (close to risk free) return with increasingly risky returns.

But I think one should try to build a model of the risk appetite, which is to say  a model of the wealth process.  This would be a rather complex process.  Stochastic no doubt, and with feedback from the actual experienced output of your core investment model.  It is much grander (much more destined to failure too) than knocking off a perpetuity to pay for your children's university bill.

Before doing that, it might be worth thinking if there are any macro or qualitative insights which might be gleaned by thinking about a world where everyone, rich and poor, operated a wealth process.  Are there implicit biases in the behaviour of investors based on how wealthy they are?  Secondly, how distributed is wealth?  How does that matter?

crescet and titubit

The speed with which one's wealth grows, and its absolute level, are tied to one's life style (one's consumption of one's income).  A useful simplification is to assume one's income derives largely from one's wealth.  Economically, this is almost completely unreasonable, since it applies only to a vanishingly small fraction of humanity.  One then needs to spend to live from this wealth.  There are however minimal quality of life spends which may imply several modalities in the relation between the wealth growth process and the spend process.  I assume for simplicity that wealth is sufficiently large that the income spent can be made in a way which still leaves wealth growing.  Put another way, there is an assumption that the wealth process grows faster than both inflation and the daily consumption of your lifestyle.   A second critical threshold is for now also ignored - as with the case where the lifestyle spend significantly impacts the wealth process, transaction costs also can incur a third hurdle to overcome.  These assumptions clear away much of the thrust of the Darst book on asset allocation.

Next, an implicit starting assumption is that wealth at time $t$ may be considered as residing in one or more currency (short term fixed income) buckets.  One then imagines that the mean value theorem can be applied to the act of taking financial risk above this risk free (globalist) position.  That is to say, in equilibrium, the entirety of the job of strategy allocation and capital deployment can be waved away as solved for now, and modelled as a single 'bet' over an appropriate time frame, whose outcome can be a win or a loss.  One then determines the ideal bet size, per unit of time, based on the mathematics of Gambler's Ruin.  That is to say, that the average bet size can be no bigger than some fraction $\delta$ of wealth at point $t$ if volatility (and long term, ruin) is to be avoided.

Of course, in reality, the complete opposite applies with titubit.  Bet sizing is often ignored and instead one's lifestyle generates the major driving constraint to investment returns variance tolerance.  In short, our lack of funds makes us bet too big - this together with transaction costs, destroys our wealth.