Fink was taught piano from the age of seven[1][2] In Frankfurt he took organ lessons with Helmut Walcha and learned conducting with Kurt Thomas.

[6] He was a member the jury of the Rheingau Musik Preis, together with Rolf Beck (Artistic Director of the Schleswig-Holstein Musik Festival), Leo-Karl Gerhartz (retired Music Programme Director of the state broadcaster Hessischer Rundfunk and Peter Hanser-Strecker (Board Chairperson of Schott Music).

[3] For the Rheingau Musik Festival, Fink initiated in 1990 an annual Komponistenporträt, the presentation of a living composer and his or her work.

[2][4][14] Fink was the personal contact to the composers and a sponsor of the concert series, presenting the composers and their music: György Ligeti, Mauricio Kagel, Kirchner, Wilhelm Killmayer, Rihm, Dieter Schnebel, Aribert Reimann, Helmut Lachenmann, Karlheinz Stockhausen, Hans Werner Henze, Krzysztof Penderecki, Steve Reich, Sofia Gubaidulina, György Kurtág, Arvo Pärt, Henri Dutilleux, Heinz Holliger, Hosokawa, Rodion Shchedrin, Kaija Saariaho, Hans Zender and Péter Eötvös.

[15] His 80th birthday was celebrated in a concert of the Rheingau Musik Festival at Schloss Johannisberg on 16 August 2010, with compositions of five composers including three premieres, works by Kirchner, Rihm, Hosokawa, Lachenmann and Jörg Widmann for clarinet, percussion, piano and saxophone.

The title of Hosokawa's composition for soprano saxophone and piano, percussion ad libitum, is Für Walter – Arc Song II.