In that sentence "profitable" is an adjective. The Latin phrase "ex ante" can be used either as an adjective or an adverb, but since what it is modifying is the adjective "profitable" and since we routinely use adverbs to modify adjectives without any hyphenation, there'd be no call for a hyphen just like there is no call for a hyphen in "highly intelligent man" or "wildly wonderful woman" or "fast approaching car" or "most famous friend," which examples are different than, say, "dirt-encrusted shoe" and "pizza-sauce orange," which instead of employing an adverb modifying an adjective, employ a noun adjunct modifying either an adjective or another noun adjunct.

I would, however, italicize "ex ante," though, seeing as how the very reason italicization was invented was to point to phrases in Italian and Latin, hence the name, so I'd go with Option A and write:

There is no ex ante profitable strategy.

In that sentence "profitable" is an adjective. The Latin phrase "ex ante" can be used either as an adjective or an adverb, but since what it is modifying is the adjective "profitable" and since we routinely use adverbs to modify adjectives without any hyphenation, there'd be no call for a hyphen just like there is no call for a hyphen in "highly intelligent man" or "wildly wonderful woman" or "fast approaching car" or "most famous friend," which examples are different than, say, "dirt-encrusted shoe" and "pizza-sauce orange," which instead of employing an adverb modifying an adjective, employ a noun adjunct modifying either an adjective (in this case, a participle being used as an adjective) or another noun adjunct.

I would, however, italicize "ex ante," though, seeing as how the very reason italicization was invented was to point to phrases in Italian and Latin, hence the name, so I'd go with Option A and write:

There is no ex ante profitable strategy.

In that sentence "profitable" is an adjective. The Latin phrase "ex ante" can be used either as an adjective or an adverb, but since what it is modifying is the adjective "profitable" and since we routinely use adverbs to modify adjectives without any hyphenation, there'd be no call for a hyphen just like there is no call for a hyphen in "highly intelligent man" or "wildly wonderful woman" or "fast approaching car" or "most famous friend."

I would, however, italicize "ex ante," though, seeing as how the very reason italicization was invented was to point to phrases in Italian and Latin, hence the name, so I'd go with Option A and write:

There is no ex ante profitable strategy.

In that sentence "profitable" is an adjective. The Latin phrase "ex ante" can be used either as an adjective or an adverb, but since what it is modifying is the adjective "profitable" and since we routinely use adverbs to modify adjectives without any hyphenation, there'd be no call for a hyphen just like there is no call for a hyphen in "highly intelligent man" or "wildly wonderful woman" or "fast approaching car" or "most famous friend," which examples are different than, say, "dirt-encrusted shoe" and "pizza-sauce orange," which instead of employing an adverb modifying an adjective, employ a noun adjunct modifying either an adjective or another noun adjunct.

I would, however, italicize "ex ante," though, seeing as how the very reason italicization was invented was to point to phrases in Italian and Latin, hence the name, so I'd go with Option A and write:

There is no ex ante profitable strategy.