When Jeff Bezos, then a New York hedge fund employee, decided to start Amazon in 1994, he quickly moved to the West Coast. So did Mark Zuckerberg, who moved from Harvard to California in 2004 to find the technology talent and financing needed to build up Facebook.

Today, the West Coast exerts a similar tidal pull for start-up companies in finance. Nine of the 15 US financial technology “unicorns” — companies worth $1 billion or more, as tracked by CB Insights — are in the San Francisco area. These Bay Area companies, which are not public, include the online payments processor Stripe, the online lender Social Finance and the finance website Credit Karma.

For the past seven years, a New York business-backed programme — the Fintech Innovation Lab — has been working to stem that West Coast tide by helping financial services start-ups sell their services in New York in an industry where the city clearly dominates: big banks and other finance companies. The programme’s backers include Henry Kravis, a co-chief executive of the private equity firm Kohlberg Kravis Roberts; Fred Wilson, a co-founder of the venture capital firm Union Square Ventures; and James D. Robinson III, a former chief executive of American Express.

“There’s no reason New York should not be the fintech capital of the world,” said another programme backer, the internet entrepreneur Kevin Ryan. He is a former chief executive of the online advertising pioneer DoubleClick and a founder of the flash-sale platform Gilt Groupe and the business news website Business Insider.

The term “fintech” covers a group of start-ups, often funded by venture capital investors, that aim to apply new technology in areas like online lending, investing and payments. These start-ups have surged in popularity among investors as banks have had to focus on complying with regulations and rebuilding capital.

The Fintech Innovation Lab is a so-called accelerator that annually gives a half-dozen start-ups the chance to interact with top financial firms, hone their products and learn how they can fit into what Accenture, a management consultant, estimated was a $270 billion technology budget for banks worldwide. Tim Estes, the president of Digital Reasoning in Nashville, which uses artificial intelligence to spot compliance and reputational risks for banks in routine employee emails, said that going through the lab programme in 2012 was “transformative for the company, opening up doors across Wall Street as advertised”.

The New York lab is one of hundreds of incubators and accelerators that have sprang up throughout the US to help start-ups, such as Y Combinator in Mountain View, California; Techstars in Boulder, Colorado; and Plug and Play Tech Center in Sunnyvale, California. Though many programmes require start-ups to give them an equity stake of 5 per cent or more, the New York lab gets only 0.5 per cent.

The lab began in 2010 as a way to bolster the New York City economy after the 2008 financial crisis. It is co-sponsored by Accenture and the Partnership Fund for New York City, an arm of the non-profit Partnership for New York City — a business-backed civic group formed in 1979 by David Rockefeller. The lab is designed for companies that want to become partners with big financial institutions, rather than compete with them.

One goal, said Robinson, an investor at RRE Ventures since 1994, is to “expose the big banks and insurers to early-stage companies doing interesting things in this area.”

Jean Donnelly, the executive director of the Boston accelerator Fintech Sandbox, said, “New York has come up pretty quickly as No. 2” behind Silicon Valley in fintech venture investments. Accenture says data from CB Insights indicates that Silicon Valley’s lead in fintech debt and equity financing has narrowed.

In 2012, the gap was 4.5-1, as valley fintechs raised $1 billion against $225 million for New York fintechs. In 2016, the gap was just 1.1-1, with $2.65 billion for Silicon Valley and $2.41 billion for New York.

Some West Coast venture investors acknowledged the city’s progress. The gap between Silicon Valley and New York has narrowed, said Pat Grady, a partner who focuses on fintech at Sequoia Capital in Menlo Park, California.

But he added: “If you want to build the next Apple or Airbnb, you come to Silicon Valley. The unmatched talent, risk-taking culture and relentless optimism mean that you have a better chance of outsize success here than anywhere else in the world.”

New York can be fertile ground for “business to business” start-ups selling to banks, Grady said. But some of the largest US fintechs, like Social Finance and Credit Karma, cater directly to consumers and have potentially larger markets, he said.

So how does the Fintech Innovation Lab work? Every year, the staff and a sponsor committee choose 20 to 25 start-ups from more than 100 applicants to meet with about 35 banks and other sponsoring institutions. The sponsors, in turn, collectively choose six to eight winners for the three-month programme.

Banks that once had to be “browbeaten” to participate in the lab are now waiting in line to check out the start-ups, said Matt Harris, a partner in Bain Capital Ventures. Lately, out-of-town banks like KeyBank in Cleveland and US Bank in Minneapolis have joined. Companies selected to participate this year included Cutting Edge, Nova Credit and BehavioSec.

Cutting Edge, a cybersecurity firm, helps protect customers’ locations and identities on the internet. Nova Credit processes and provides credit data from foreign institutions on individuals so banks can lend more readily to immigrants. BehavioSec helps confirm customer identities by analysing how they type, click and swipe on their devices.

The lab featured 19 events over three months, including meetings with Kravis and James Gorman, the chief executive of Morgan Stanley. Kravis stressed the importance of company culture, and Gorman fielded questions about Wall Street’s use of artificial intelligence and how investment banks do business with start-ups.

There was also a practice pitch session at the office of the private equity firm Warburg Pincus. This year’s lab culminated with a Demo Day on June 22 at a packed 215-seat auditorium at Bank of America’s New York office.

Each entrepreneur was introduced by a Wall Street mentor and then gave a brief pitch for his business. Robinson and other venture investors strolled a hall with exhibit tables for each start-up. David Reilly, a senior technology executive at Bank of America, said the programme was useful because big banks “can be exceptionally difficult to sell to.”