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I would probably go for some middle ground such as if (year > 0) then shares * Square root (years).

Just because someone has held a stock for 20 years does not necessarily mean they are currently interested in the long term. But, it probably points in that direction.

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You might want an upper limit, so either logistic growth [1] or something like 1 - exp(-(T + T_0)) feels like it makes more sense.

I especially like logistic growth for having slow growth at the start and end, only growing quickly in the middle.

[1] https://www.khanacademy.org/science/biology/ecology/populati...

You don't need an upperbound as long as your function is sufficiently slow growing.

Example:

Log(years) doesn't have a bound, but is unlikely to cause problems over any reasonable time scale.

Or it means they are so utterly passive and unthinking that they are just the voters entrenched management dreams about.

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