GENEVA — Thierry Stern looked pleased when, in an interview in early December, he said 2019 would be a record year for Patek Philippe.

“I’m not running after records every year, though,” Mr. Stern, the chief executive, said, declining to detail the company’s turnover. “This is the beauty. We don’t have any shareholders. We don’t care.”

Patek Philippe has been in the hands of the Stern family since 1932 and, despite repeated reports of interest from major luxury groups, is still independent. It does not make its financial results public, but according to estimates by the Swiss private bank Vontobel, in 2018 it had sales of 1.45 billion Swiss francs ($1.49 billion), making it Switzerland’s fifth-largest watch company.

But unlike the four ahead of it, a list that is topped by Rolex and Omega, Patek Philippe’s output is small in comparison. Mr. Stern says Patek makes 62,000 watches a year. Rolex is believed to make more than a million.

Mr. Stern, who succeeded his father, Philippe Stern, as president in 2009, said his ambition was to grow the company by no more than 3 percent each year. “If the economy’s not so good, we can decrease also,” he said.

But there is little sign of retreat. In 2005, when I first interviewed Mr. Stern and his father, he said the company was making 30,000 watches a year, less than half the current figure.

And, Mr. Stern said in December, the company employed 460 people in 1996 when it moved to its headquarters in the Geneva suburb of Plan-les-Ouates. That number has risen to 1,600, with 600 more staff members worldwide.

To accommodate the growth, the company already has moved into part of a sprawling almost 1.2 million-square-foot building being finished alongside its headquarters. Mr. Stern said the company funded the construction cost of more than one billion Swiss francs, adding with a wry smile, “We don’t like banks.”

While there have been some changes, Mr. Stern, 49, said he continues to follow in his father’s footsteps. “It was clear for me and my Dad that we should keep the same strategy,” he said, although Patek has benefited from digital tools like Instagram. In the 2005 interview, he said, “we are not a fashion brand,” an approach he has maintained.

Last year there were news reports that Rolex wanted to buy Patek. “I think I made it quite clear that I will not sell,” Mr. Stern said. “We should be proud of it when big companies want to buy Patek because that means we are doing something right. But we are not for sale.”

Instead, he said, he intends to be at the company for what he called “many years” before offering the keys to one of his two sons. The elder, at 18, is studying for the hospitality industry, but the younger, who is 16, has just started studying watchmaking and working part time at the factory.

“I didn’t have two children to take over Patek,” Mr. Stern said. “They have to make their own choice. We will always find somebody that will take care of Patek Philippe.”

Looking to the next decade, Mr. Stern said that he had no plans to expand into new territories and that he was not pushing hard in China, which his competitors have identified as critical to traditional watchmaking’s long-term success. According to the Federation of the Swiss Watch Industry, Swiss watch exports to mainland China rose 32.8 percent from 2016 to 2018. Patek opened its first branded showroom in Shanghai in 2005.

“I’m not afraid to stay behind,” Mr. Stern said. “We are already in 74 countries. I don’t have the capacity, and I would not destroy another market just to shift watches to China. But also, we go step by step. This is how we do our business. It’s worked in the whole world.”

He said the approach had protected Patek’s business when markets have declined. In December, for example, the federation reported that exports to Hong Kong, which it lists separately from mainland China, were down by 26.7 percent in November year over year, eroded by the city’s continued civil unrest and related economic recession.

“Hong Kong has not really affected us,” Mr. Stern said. “We are down maybe 30 percent, which is quite good. Some brands are down 70 or 80 percent. That’s a disaster. But that’s their mistake. They were focusing too much on Hong Kong.”

If he has a concern, Mr. Stern said, it is the rise of what the watch industry calls “flippers,” buyers who purchase high-demand watches to resell them at a premium, a practice he says he wanted to curtail. But he said he was not working with retailers to solve a problem in which prices of pieces such as Patek’s steel Nautilus have skyrocketed on the pre-owned market, sometimes to more than double list price.

“Maybe sometimes the retailers are part of it,” he said, but he does not lay all the blame at their doors. “We buy back a lot of watches every year from the secondary market, because we want to know why a watch is for sale.”

However, he said that if the company learned that a retailer is selling watches to customers involved in such resales, and the retailer did not prevent such activity, the company would end the retailer’s Patek account. “If I have the proof, then I act,” Mr. Stern said.

He said rising prices in the primary market had changed Patek Philippe’s customer profile. “We are losing so many people who are enjoying watches, because they cannot afford it anymore,” he said. “But we are also gaining a whole new young generation who are very successful, made a lot of money and who are willing to invest in Patek. That has really changed.”

Mr. Stern remains bullish about his company’s fortunes.

“I don’t see why Patek Philippe should be in danger as long as we are very careful,” he said. “The tough part is to stay independent.”