My abbreviated version of my "over time" and "into the tails" comment omits the "over time" part, in case that wasn't clear.

Tightened up:

If μ > r, then for any {ε > 0, ζ > 0} there exists a put option P_t(S,X,T) such that Pr{P_T(S,X,T) > 0} < ε and E{P_T(S,X,T)} < ζ P₀(S,X,T).

An abbreviated version of the same statement, mostly in formulas:

If μ > r, then for any {ε > 0, ζ > 0} there exists a put option P_t(S,X,T) such that Pr{P_T(S,X,T) > 0} < ε and E{P_T(S,X,T)} < ζ and P₀(S,X,T) > e^-rTE{P_T(S,X,T)}.

(This within Black-Scholes assumptions.)

Then there are all manner of trading strategies that are almost surely profitable beyond the riskless interest rate, with some combination of "over time" and "into the tails."

I read your last comment incorrectly, and responded incorrectly.

I would say that µ < r is not relevant to two-dimensional Markowitz criterion, which is not what you asked.

If µ > r, buy the stock all day long, at least within the parameters of the model.

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Is there that volatility adjustment formula or was I not careful enough? I've got problems with understanding plain English (and other languages), only formulas are sufficiently clear for me. No volatility adjustment formula as such. From the appendix, there is σ’=sqrt[2(r−µ)], but this refers to t...

Maybe you read too much into things and think too little.

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Pickleball. Why?

So old, out-of-shape people can get a little exercise.

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"Conservatism consists of exactly one proposition, to wit: There must be in-groups whom the law protects but does not bind, alongside out-groups whom the law binds but does not protect." -- Frank Wilhoit, musical composer