Who are the contemporary -not necessarily living- philosophers whose view of the world is similar to Schopenhauer's?
In terms of the pessimistic, anthropophobic aspect of Schopenhauer's philosophy, Ulrich Horstmann surely is one of his strongest living followers, though his writings are rather essayistic than scholarly philosophical. (Unfortunately, none has been translated into English as far as I know.)
Horstmann even critizises Schopenhauer for being not radical (that is, as he calls it: "anthropofugal", meaning fleeing from mankind) enough. Wikipedia correctly sums up his main theory:
(At this point, one might suspect that he is using exaggeration and satire as means to put forth a Foucaultian criticism of humanist, enlightenment contradictions. He would certainly reject that but you could argue that would still be part of the show.)
In one of his central works, Das Untier ("The beast"), he introduces the main thoughts of Schopenhauer and praises some other pessimistic philosophers or cultural theorists he believes to be (at least partly) equals, like Foucault, Freud, Koestler and especially Philip Mainländer and Eduard von Hartmann (died 1876 and 1906 so not really contemporary).
There are two philosophers whom Horstmann by and large considers as fellow anthropofugal thinkers so they might be worth checking out in case you do not know them already, both already dead but could be maybe regarded contemporary: Emile Cioran and Günther Anders.
To complete this answer, here’s a brief bibliography of contemporary philosophers close to Schopenhauer (very pessimists or antinatalists) : In english : David Benatar : Better never to have been (2006) Jim Crawford : Confessions of an antinatalist (2010) Thomas Ligotti : The conspiracy against the human race (2011) In french : Annaba : Bienheureux les stériles (2002) Théophile de Giraud : L’art de guillotiner les procréateurs : manifeste anti-nataliste (2006) Roland Jaccard : La tentation nihiliste (1989) In german : Karim Akerma : Verebben der Menschheit ? Neganthropie und Anthropodizee (2000) In portuguese : Rafael Tages Melo : A última filosofia : an essay about antinatalism (2012)