Olga Koch and Finlay Christie use their privilege as a rich seam of humour | Brian Logan

At a festival where everyone’s losing money, and some can’t afford to come in the first place, how do you talk about your wealth and privilege? (Far less invite people to laugh about it?!) I’ve seen fringe shows address privilege in the past. Jack Whitehall, Ivo Graham , Will Smith (The Thick of It’s co-writer, not the slap-happy megastar): these acts broached their poshness, but seldom looked beyond the superficial class signifiers. And even then, they were doing so before the cost-of-the-fringe crisis reached, as it has in the last few years, boiling point.

To pull it off now, you’d need a lot of charm, or a conspicuous slice of moral seriousness. In his new show, I Deserve This (★★★★☆), Finlay Christie has one, and in hers, Olga Koch Comes from Money (★★★★☆), Koch has the other. I first encountered Christie at the fringe two years ago , as one of the first wave of stars arriving on stage from TikTok . He won the prestigious So You Think You’re Funny prize aged just 19, and amassed industrial quantities of online followers in his early 20s – so there was always something gilded about his rise, even before he introduced generational wealth into the mix.

In his new show, as in his first, that privilege feeds into Christie’s pleased-with-himself persona: a reflex flippancy, as if it would be vulgar to take anything seriously. But he makes it work, because he marries it to some light-touch cultural commentary (on the things we need to do these days to acquire social capital), writes a mean joke, and self-deprecates with good grace.

I Deserve This does not address privilege as directly as Koch’s show, but Christie’s wealth orients him in a particular way towards his subject: the things young people need to say, do and claim these days to boost their social standing. It gives him anthropological distance: he surveys the absurdity of it all from the impervious vantage point of a man spared struggles of his own. (“When I have Vietnam flashbacks, they’re of a nice holiday.”) And so the show tours through trauma, neurodiversity and so on, illustrated with reference to our host’s life: the time he had sex with a man just to look cool; the racism test he undertook when in a mixed relationship; his fondness for UK grime, based on identifying with precisely half the lyrics of every song.

I found the show’s combination of intelligence and pleasingly black-hearted wit just so. Others may see the same old glib, posh-boy humour, with Christie putting nothing on the line. (Not strictly so: as he acknowledges, his bucket speech rings hollow at the end, so income is bound to take a hit.) Certainly, Olga Koch works harder to extricate herself from the channels down which supercilious rich-person comedy usually runs. Her show interrogates the myths around money, and having it. Is wealth ever deserved? What is its moral dimension? Is its distribution rational in any way?

All of this is filtered through Koch’s life, which fortunately intersects with three different financial systems: that of a collapsing Soviet Russia, where she grew up; then the US, where she worked; and now the UK’s. She is explicit about her own privilege (“The thing about being on a yacht …”), but not that explicit: a routine about being asked “How rich?” coyly withholds actual figures. That stands out only because coyness isn’t Koch’s usual mode: in what she refers to as her “bad bitch” character, she’s declamatory here, always flamboyantly on the attack, recounting her pampered youth, her young adulthood working for “the video platform that radicalises teenagers”, her holidays on Jeffrey Epstein’s island. Just kidding? Our uncertainty is part of the fun.

In one of her neatest jokes, Koch says that talking on stage about being rich “is the hardest thing I’ve ever done”. Interesting, then, that she momentarily loses confidence in the “bad bitch” character midway, stepping out of it to check we’re in on the joke. Even Koch, whose project is all about considering money objectively, separating it from shame (or pride, for that matter), remains vulnerable to the ick and the awks of publicly addressing it. Her show ends by confronting the moral question around how her family wealth was acquired in the asset-stripping frenzy of the USSR’s collapse, whether she should upbraid her parents about that – and with an update on her dad’s relationship with Putin’s Russia. It also closes, not with a bucket speech, but a fundraising drive for the charity Arts Emergency , which works to widen access to the arts. Checking one’s privilege was seldom so comprehensively undertaken – and in both these shows, very entertainingly, too.

• Olga Koch Comes from Money and Finlay Christie: I Deserve This are both at Monkey Barrel Comedy, Edinburgh, until 25 August