A few weeks after she realized her husband was finally leaving her, Sarah Pursglove flew down to the Bahamas to figure out how much money he really had. Like many women married to very wealthy men, she didn’t know much about the family accounts. Her husband, a Finnish entrepreneur named Robert Oesterlund, had sworn to a Canadian court that his immediately calculable “net family property” totaled just a few million dollars. Pursglove was skeptical. She could come up with several family purchases worth more than that off the top of her head. There was the 165-foot yacht, Déjà Vu — that cost a few million dollars a year just to keep on the water. There was the $30 million penthouse at the Toronto Four Seasons, which was still being renovated. It wasn’t their only home. The Déjà Vu wasn’t even their only yacht.

Pursglove grew up in a working-class family. She did not consider herself to be a complicated person, or a greedy one. Recent events in her life had, however, inculcated a newfound habit of suspicion. Her husband’s tirades, his frequent absences and threats to leave, had led inexorably to the day when she tailed him through the streets of Toronto and caught him picking up an interior designer for what appeared to be a romantic ski getaway. She had been with Oesterlund since she was 25 and scraping by as a cruise ship’s photographer. Now, as she assessed her crumbling marriage and girded for divorce, she wondered what else she didn’t know.

Her first answers came that morning in the Bahamas, as she quickly rifled through papers in their soon-to-be-former vacation home. She didn’t have long: The caretaker, Pursglove suspected, was loyal to her husband and would soon alert him that she was there. In a pile of mail was a statement from a bank in Luxembourg showing an account with at least $30 million in cash. She had never seen it before. There were two laptops — one with baby photos of their younger daughter, which she set aside. In a cupboard were documents concerning not only Xacti, the internet company she and Oesterlund had built, but also oddly named corporations in other states and countries. Finally, there was a statement from their accounting firm. She had never seen that before, either. The accountants seemed to think her husband was worth at least $300 million.

But even as Pursglove was repacking her suitcase for the flight home, her family’s fortune was vanishing into an almost impenetrable array of shell companies, bank accounts and trusts, part of a worldwide financial system catering exclusively to the very wealthy. In recent decades, this system has become astonishingly effective at “offshoring” wealth — detaching assets, through complex layers of ownership and legal planning, from their actual owners, often by hiding them in another country. Created by lawyers, accountants and private bankers and operating out of a global archipelago of European principalities, former British colonies and Asian city-states, the system has one main purpose: to make the richest people in the world appear to own as little as possible.