Manfred comments on A hypothetical question for investors

[Manfred]

For an interesting related problem, look up Kelly betting.

[solipsist]

Also Intertemporal portfolio choice.

Intertemporal portfolio choice is the process of allocating one’s investable wealth to various assets, especially financial assets, repeatedly over time, in such a way as to optimize some criterion.

[solipsist]

Or, more generally, the Wikipedia article on Intertemporal portfolio choice.