HONG KONG — Ever since Anbang Insurance Group bought the Waldorf Astoria hotel in New York nearly three years ago, the politically connected company has tested the mostly unwritten rules of the Chinese business world, ignoring regulators’ hints and wading into international controversies.

Now, with the detention by police of Anbang’s chairman, the biggest question is which potential transgression may have spurred Beijing to crack down.

The chairman, Wu Xiaohui, has not been publicly accused of any wrongdoing, and the authorities in China sometimes detain financiers for questioning only to release them to resume their duties a few days later. Anbang said on its website on Wednesday only that Mr. Wu was temporarily unable to fulfill his duties as chairman for “personal reasons.”

Anbang embodies the contradictions of China’s modern economy, with its potentially combustible mix of risk-taking capitalism and episodically draconian government control. Abroad, Anbang shocked Wall Street with its multibillion-dollar takeover efforts, even as Beijing moved to rein in deals. At home, it drew tens of billions of dollars from Chinese investors big and small looking for their own success stories — making it vulnerable at a time when Beijing is looking to limit potential financial explosions. And it played the fraught game of politics on both sides of the Pacific, including courting Jared Kushner, the son-in-law of President Trump.

On paper, the company appeared to be a quiet, conservative insurer. But Anbang often seemed to behave as though the usual informal political guidelines did not apply — possibly because Mr. Wu was married to a granddaughter of Deng Xiaoping, a major Communist Party figure who was China’s paramount leader in the 1980s.

“One of the basic rules of operating in China is everybody is a dog on a leash,” said Fraser Howie, a former banker in Asia who has co-written three books on the Chinese financial system. “Nobody has freedom. The party does not give anybody freedom. They merely give them a leash.”

One bright line for Chinese companies: Try not to get mixed up in China’s foreign policy without clear backing from Chinese leaders.

Yet Anbang tried late last year to invest in an office building partly owned by Mr. Kushner. The potential investment, which was never consummated, became controversial in the United States because of Mr. Kushner’s role in setting China policies in the Trump administration, and exposed Beijing to accusations that it was trying to meddle in American politics. No Chinese bank stepped forward to play any role in a possible transaction.

Some analysts in China said that political considerations were likely to be the main reason that Beijing had detained Mr. Wu, pointing to a Communist Party meeting scheduled for late this year at which party officials are to consider changes in leadership. Anbang has a murky ownership structure that traces back to family and friends of Mr. Wu who live on apparently modest means, fueling speculation in China that other wealthy and powerful figures may be behind it.

By detaining Mr. Wu and other high-flying business figures, said Zhang Lifan, a Beijing-based historian and the son of a food minister under Mao Zedong, Communist Party leaders are sending a powerful message to potential rivals that they won’t brook dissent. “You can prevent your opponents from making their moves,” he said.

Anbang also pushed — and even defied — the government’s often loosely defined limits on what Chinese insurers are allowed to do.

The company was among a number of Chinese insurers unshackled by regulators earlier in the decade and allowed to invest in a wide range of areas. Anbang was among the most aggressive. After acquiring the Waldorf Astoria, it engaged in a number of high-profile global deal efforts, including an ultimately unsuccessful campaign to buy Starwood Hotels and Resorts Worldwide.

That campaign continued even after the Shanghai stock market crashed in the summer of 2015, which prompted the Chinese government to begin stepping up its measures to discourage companies and individuals from taking large sums of money out of the country. Just last week came the disclosure that, starting in September, banks will be required to send daily reports to the government on every overseas credit card expenditure by their customers of more than 1,000 renminbi, or $147.

The effort also tested the rules set by Chinese insurance regulators, who say no insurer may put more than 15 percent of its assets overseas. According to Anbang’s most recent financial disclosure this spring, nearly three-fifths of the assets of its main business, life insurance, were overseas. But the rule is poorly defined on crucial questions of how to compare overseas assets to an insurer’s overall assets.

Anbang has also argued that it did not depend on converting renminbi into foreign currencies to make its acquisitions, but has not explained how it was able to finance so many foreign deals without converting large sums.

To fund its investments, Anbang aggressively marketed what in China are called wealth management products. Wealth management products are often short-term investments that offer investors considerably higher rates of return than are paid on bank deposits. While they are often sold out of the offices of banks and securities brokerages, giving investors a sense of confidence, the money often goes off the balance sheets of banks and into murky and sometimes speculative investments.

Anbang’s wealth management product sales contributed to eye-popping growth. In the six years through last December, the assets of Anbang’s life insurance unit multiplied 2,876-fold, to $213 billion. Anbang also has a much smaller property and casualty insurance business.

But wealth management products have drawn growing concern from regulators, who worry that they could fail and shake China’s brittle financial system. Early last month, China’s insurance commission banned Anbang from selling two of its investment products, one of them because it had been portrayed to regulators as a long-term investment when it was actually for two years. The other product had a regulatory filing that was missing the signature of an actuary.

“The nature of insurance should be safety, mobility, and the least concern is yield,” said Ju Lan, the director of the risk management and insurance research center at the HSBC School of Business at Peking University. “Since we don’t allow insurance companies to go bankrupt, once one gets into trouble, the government need to save it.”

After the detention of Mr. Wu, investors in Anbang wealth management products lit up social media starting on Tuesday night with questions about whether to leave their money with the company or to demand it back immediately, incurring significant penalties for early redemption.

“I am worried something big will happen and I won’t get my money back,” wrote one investor. “Yet it costs a lot to quit as well.”