There aren't many public records about who bought art made by Balthus, and his works rarely reach the open market. but that's probably because of what the art depicts...

Balthus

Painting http://cdn2.all-art.org/DICTIONARY_of_Art/b/balthus/Untitled-1.jpg

With his cat http://d2jv9003bew7ag.cloudfront.net/uploads/Balthus-the-artist-with-his-cat-Image-via-sartlecom.jpg

Painting http://www.andro.gr/wp-content/uploads/2015/09/image1.jpg

Workshop https://pbs.twimg.com/media/Cx_WL9iW8AAaSCF.jpg

Workshop https://images.newrepublic.com/33c3ed0d48458e9020f7483259570a58d5e6bab4.jpeg

With his wife https://d3hp8xnxb3lun4.cloudfront.net/wp-content/uploads/2016/08/EH_bw_port_balthus-01-b.jpg

The king of cats self portrait http://www.newyorksocialdiary.com/i/partypictures/10_01_13/jk/IMG_1641_2.jpg

Balthus his Paintings (NSFW):

Cats & Girls

Cat, girl, chair http://www.artsjournal.com/artopia/wp/wp-content/uploads/2013/09/ThereseDreaming.jpg

Humancat, girl rowing, rainbow fish https://uploads4.wikiart.org/images/balthus/the-mediterranean-cat-1949.jpg Balthus painted the large picture as a decoration for the interior of "La Méditerranée," a seafood restaurant that still operates on the Place de l'Odéon in Paris. The feasting cat is a self-portrait.

Pedophile, girl https://s-media-cache-ak0.pinimg.com/736x/3f/fb/57/3ffb5799c3e8706fa85ebf2897ad37c8.jpg

The guitar lesson https://mydailyartdisplay.files.wordpress.com/2016/01/the-guitar-lesson-by-balthus-1934.jpg In 1977, it appeared for a month at Pierre Matisse’s 57th Street gallery. It has never been exhibited again

The moth (checkerboard, girl mirror, cat) https://uploads0.wikiart.org/images/balthus/the-moth-1960.jpg

Checker floor, girl http://www.galeriedada.com/img_big/Bal8.jpg

The business man https://s-media-cache-ak0.pinimg.com/236x/0d/2f/4f/0d2f4fbd316a0998ddf20a554e2c3fe8.jpg

Girl chair cat http://www.newyorksocialdiary.com/i/partypictures/10_01_13/jk/Untitled-6.jpg

http://www.newyorksocialdiary.com/i/partypictures/10_01_13/jk/IMG_1950_2.jpg

http://c8.alamy.com/comp/DB0F0B/visitors-observe-the-1933-painting-cathys-toilette-by-balthus-balthasar-DB0F0B.jpg

About his Muse:

"Anna Wahli (8), the youngest daughter of Balthus’s doctor, was drafted to be the model."

http://media.vanityfair.com/photos/54caa015a298661966edc657/master/h_606,c_limit/image.jpg

https://files.newsnetz.ch/story/1/4/7/14762002/8/topelement.jpg

"Anna Wahli, the youngest daughter of Balthus’s doctor, was drafted to be the model. Eight years old when she started sitting for him, she writes in an essay in the Steidl book that she was told Balthus chose her because he liked the sound of her humming Mozart. Across nearly nine years, she would show up Wednesday afternoons to pose. She remembers Balthus as being a bit of a klutz with the camera; sometimes she’d have to step in and turn it right side up.

Balthus’s widow, Setsuko Klossowska de Rola, and his daughter, Harumi, have kept a lid on the photos for more than a decade, and they would not have gone ahead with the show without Anna’s permission.

(Today she’s a psychotherapist and social worker, and it’s difficult to resist wondering if her sittings with Balthus led to her choice of profession.) The backing of all three women is important because of the content of the photos. Anna is dressed in either a tartan or a white dress when she is younger, typically posing in an armchair, but as time goes on she moves to a chaise longue and wears a brocade robe that sometimes falls open, so she’s partially nude. These images are raw, and true, and risk being fodder for the censors who seem to rear their heads whenever children appear nude in art photographs, even when there is absolutely nothing dodgy going on. (...)

Not that it’s inappropriate to be super-sensitive to whether these images are exploitative. Balthus’s most famous paintings often come with a purposeful sexual undercurrent, and Anna was just a child. The Polaroids have many moods: beautiful, awkwardly acrobatic, creepy, heartbreaking, luminous, timeless. They also document a meticulous artist’s obsession with capturing exactly what he was after—say the position of an arm, the way a leg might stretch, the mood created by just a shaft of light. There is probably no better record of how Balthus worked."....

From http://www.vanityfair.com/culture/2013/10/balthus-polaroids-photos-model

Polaroids of his model (NSFW):

https://hyperallergic.com/wp-content/uploads/2013/10/Balthus1.jpg

http://tabletmag.com/wp-content/files_mf/polaroid_620.png

http://www.tabletmag.com/wp-content/files_mf/reup_82057.jpg

https://s-media-cache-ak0.pinimg.com/originals/73/84/5e/73845e3830c79b876a2def29caf4bbe6.jpg

http://odlp-staging1.s3.amazonaws.com/uploads/2014/02/3_0548_LastStudy-4.jpg

"His work is where you'd expect it - in the Louvre, the Tate, the Metropolitan in New York, and in the hands of private collectors such as Billy Wilder, Mike Nichols, the Agnelli and Niarchos families. The most widely disseminated Balthus is Girl and Cat (1937), from 1989 till this month the cover of the Penguin paperback of Nabokov's Lolita. Martin Summers, his agent at London's Lefevre Gallery, advises against two things. Balthus does not like mention of paedophilia when talking about the work, and on meeting him, it somehow seems irrelevant. He is also "incensed" by biography of him by Nicholas Fox Weber, published last year, which dismisses his recent painting.

By painting The Guitar Lesson, he'd deliberately courted controversy. The image is of a sexual awakening; the aroused girl lies across her music teacher, pudenda exposed, guitar discarded. "I remember I was very poor," he says. "The only way to get out of that state was to make a scandal. It worked well, too well." (...) "

https://www.theguardian.com/culture/2000/apr/25/artsfeatures

"Record $1,185,800 Paid For a Balthus Painting" http://www.nytimes.com/1984/03/28/arts/record-1185800-paid-for-a-balthus-painting.html

"10 Artists/Entertainers Besides Woody Allen Accused of Sex Crimes—And What Happened to Their Careers as a Result" http://www.alternet.org/culture/10-artistsentertainers-besides-woody-allen-accused-sex-crimes-and-what-happened-their

More about Balthus and his art http://pijet.com/2008/06/16/the-adoration-or-perversity-of-childhood-in-balthuss-paintings/