Frans van Mieris 1. Leiden, Netherlands, 1635-1681. A cavalier (self portrait) 1657/59 oil on oak panel, 20 x 16 x 1cm. Collection of Art Gallery of New South Wales

A Cavalier a 17th-century Dutch masterpiece stolen from the Art Gallery of NSW and still unrecovered.

The police have given up and so has the Art Gallery of NSW. Four-and-a-half years after A Cavalier, a 17th-century Dutch masterpiece insured for $1.4 million, was stolen from the gallery, Australian authorities have stopped trying to recover the painting.

The self-portrait by Frans van Mieris is listed on the FBI's top 10 list of art crimes alongside Paul Cezanne's The Boy in the Red Vest, one of four paintings stolen from a Swiss museum in 2008 and valued at $91 million, which was recovered in Serbia last month.

Acting Sergeant Chris Nash said NSW police had suspended their investigation in 2008 after exhausting all avenues of investigation.

''Police cannot speculate on why the artwork was stolen other than to speculate the artwork may have been sold to a black market investor. However, no evidence exists to substantiate this,'' he told The Sun-Herald. ''It is believed the artwork may have been smuggled outside the country.''

The chief executive of the Association for Research into Crimes Against Art, Lynda Albertson, said the painting would be easy to sell.

''The world is full of art lovers with rich tastes and richer pocketbooks,'' she said.

A Cavalier measures just 20 centimetres by 16 centimetres and small works of art are easily smuggled, according to Joanna Mendelssohn from the college of fine arts at the University of NSW.

''I tend to think the AGNSW one was an opportunistic theft. If it was opportunistic, it would be hard to dispose/return the work,'' Associate Professor Mendelssohn said.

In contrast, a group calling themselves Australian Cultural Terrorists stole Pablo Picasso's The Weeping Woman from the National Gallery of Victoria in 1986 as a political protest. It was recovered 15 days later from a locker at Spencer Street railway station although the thieves were never caught.

The chairman of the Art Loss Register, Julian Radcliffe, said thieves target art because the level of security and risk of detection was low compared with robbing a bank.

He said it would be difficult for a thief to resell a well-known artwork for its true value but it could be used as security for a drug deal or perhaps sold as a copy at a fraction of its value.

The Art Loss Register, which operates an international database of stolen art, estimates that 12 per cent to 15 per cent of stolen artworks are recovered.

But Mr Radcliffe said his organisation had recovered artworks stolen 350 years ago, ''so there is always a chance''.

Cezanne's Bouilloire et Fruits was one of seven paintings stolen from a private residence in the US in 1978. It was found in 1999 and later sold for $29.3 million, while the remaining paintings were returned to the owner over the next decade.

Picasso's Woman in White Reading a Book was unearthed in 2005, 65 years after it was stolen.

The Art Loss Register lists Picasso as the most stolen artist, with 1147 paintings registered as stolen, missing or disputed. In January, three paintings, including Picasso's 1939 Woman's Head, were stolen from Athens' National Art Gallery.

Thieves also favour artworks by Nick Lawrence, Marc Chagall, Karel Appel and Salvador Dali, according to the database.

Mr Radcliffe estimated the worldwide value of artwork stolen each year at £1 billion ($1.6 billion).

He said the majority of art was stolen from European countries such as Italy, where much artwork is held in poorly protected churches.

Significant thefts have also occurred at archaeological sites in the Middle East and Thailand.

''In the USA, very little art is stolen since their museums and galleries have good security,'' Mr Radcliffe said.

In contrast, A Cavalier was screwed to the wall with two visible keyhole plates and was situated in a room with no camera surveillance and a guard intermittently present.

The former Art Gallery of NSW director Edmund Capon said the NSW government, then led by Morris Iemma, ignored warnings about the gallery's inadequate security.

''We were very conscious of the fact we were understaffed and had no technology in terms of security and yet we had all these priceless paintings,'' he told The Sun-Herald in 2010. ''That situation has been rectified but it should have been rectified without having to pay that price.''

The Australian Museum is trialling technology that will allow guards to monitor security from mobile phones. A spokeswoman, Christine Callen, said the museum had no deficiencies in security but declined to outline measures to prevent theft.

In 2007, a former employee was jailed for seven years for stealing more than 2000 skulls, skins and skeletons - worth an estimated $873,250 - over four years from the Australian Museum.

Art theft continues to plague major cultural institutions and private collectors in Australia.

In 2011, the National Gallery of Victoria reported the theft of a 19th century painting, valued at $200,000, which went missing in 1999 during renovations at the gallery's St Kilda Road premises.

In August 2010, 18 works worth $2 million were stolen from the Darling Point penthouse of the millionaire developer Peter O'Mara.

A spokeswoman for the NSW police said their investigation into the theft was suspended.