Another possible small future tweak to the lifetime consumption utility calc

In a recent post How I might tweak my consumption utility simulator in the future, I was casually ruminating on how I might adapt my lifetime consumption utility simulation in the future to factor in some additional considerations like bequest, spend shocks and foregone optionality. I ran across another one I might want to try when reading Davidoff et al. "Annuities and Individual Welfare" (2003) They replace the period consumption term c(t) with c(t)/s(t) where s(t) allows the modeler to shape an "internal habit" to the consumption path. To quote in order to help with the definition of this idea: 

What differentiates our more general setup from prior work is that we can vary s(t) in equation (1) so that the utility function exhibits an “internal habit,” which we can then adjust to create optimal consumption trajectories that differ markedly from the usual CRRA case. The intuition behind our utility function, taken from Diamond and Mirrlees (2000), is that it is not the level of present consumption, but rather the level relative to past consumption, that matters for utility. For example, life in a studio apartment is surely more tolerable for someone used to living in such circumstances than for someone who was forced by a negative income shock to abandon a four-bedroom house. In choosing how to allocate resources across periods, “habit consumers” trade off immediate gratification from consumption not only against a lifetime budget constraint, but also against the effects of consumption early in life on the standard of living later in life. Following Diamond and Mirrlees (2000), we model the evolution of the habit as follows:

[alpha] is the parameter that governs the speed of adjustment of the habit level. When [alpha] is zero, the habit is constant and we are back in the additively separable case. As [alpha] approaches infinity, present habit approaches last period’s consumption.