Ms. Wang is known as the driving force and general director behind the couple’s Long Museum, which has two branches in Shanghai. Over more than 20 years, the two have amassed an extensive collection of mostly traditional and contemporary Chinese art, much of it on display in the museums. Days after their latest blockbuster purchase, Mr. Liu and Ms. Wang were back at it, flying to Beijing to attend the fall sales of a top auction house, China Guardian. They said their goal was to transform the Long Museum into a world-class destination that could compete with the likes of the Museum of Modern Art and the Guggenheim Museum in New York. Advertisement Continue reading the main story And nothing, Mr. Liu said, says world class quite like a Modigliani nude. “Every museum dreams of having a Modigliani nude,” Mr. Liu said. “Now, a Chinese museum has a globally recognized masterpiece, and my fellow countrymen no longer have to leave the country to see a Western masterpiece. I feel very proud about that.” He added, “The message to the West is clear: We have bought their buildings, we have bought their companies, and now we are going to buy their art.” With his acquisition of the nude, a 1917-18 canvas known as “Nu Couché,” that message certainly seems to have gotten across. “This purchase was a proclamation of his arrival,” said Thomas Galbraith, managing director of auctions at Paddle8, an online auction house. “Anyone in the art world who didn’t know his name knows it now.” Mr. Liu’s rise is a classic rags-to-riches tale of post-Mao China. Growing up in a working-class family in Shanghai in the 1960s and ’70s, he said, he knew early on that he wanted to go into business. After dropping out of middle school, he began selling leather handbags, then saved enough money to buy a taxi. Advertisement Continue reading the main story In 1983, he was still eking out a living as a small-time businessman when he met Ms. Wang, who was working as a typist at Shanghai Normal University. By the late 1980s, with China’s economic liberalization in full swing, Mr. Liu’s fortunes turned as a series of stock market investments he had made began to take off. Today, he is chairman of the Sunline Group, a holding company based in Shanghai whose interests include chemicals, pharmaceuticals, real estate development and a financial unit. In addition to owning a stake in a pharmaceutical company, he was also an early investor in Beijing Council International Auction, an auction company in the Chinese capital started by one of Ms. Wang’s friends. According to Forbes, his assets in 2015 totaled $1.22 billion. “His decisions might seem very risky, but people forget he has spent his whole career assessing risk in the capital markets,” said Dong Guoqiang, chairman of Beijing Council and a longtime friend of the couple. China’s art market was still in its nascent stages when Mr. Liu and Ms. Wang began going to auctions and buying art in the early 1990s. Over the years, what started as a hobby became an obsession. While Mr. Liu preferred collecting traditional Chinese artworks and objects, Ms. Wang focused on acquiring art from the Cultural Revolution era and, later, contemporary Chinese art and art from throughout Asia. They began to collect Western artists as well, and their holdings now include work from Jeff Koons’s mirror-polished sculpture series. Several years ago, Ms. Wang, a self-proclaimed “art fanatic,” came up with the idea of opening a museum so they could show their collection to the public. But first, she needed to persuade Mr. Liu. “All of our friends were buying private planes, and he said he wanted to buy a plane, too,” she said. “I refused. I said let’s just put in some more money and start a museum. It will be good for Shanghai, and it will be good for the country.” So in 2012, Mr. Liu and Ms. Wang opened the Long Museum Pudong, one of many private museums that have begun in Shanghai in recent years as the local government tries to transform the city into an international cultural capital. In 2014, they opened a second branch, the Long Museum West Bund, part of a government-sponsored project to develop a waterfront cultural corridor in Shanghai that includes private museums, a large entertainment complex, and soon, the headquarters for DreamWorks’ new Chinese joint venture animation studio.