Luxury cars line the parking lot of the upscale Mandarin Plaza mall in Kyiv, while their well-heeled owners flaunt their wealth in its jewellery and designer clothes stores.

One January night in Kyiv, a company called Milton Group threw a glitzy New Year’s party for its staff. To the strains of a pop-rock cover band, contortionists and fire-dancers whirled under neon lights as young salespeople revelled in the spoils of a record-breaking year selling investments in cryptocurrencies and stocks. The firm’s management distributed cash,...