Hmmm...that is a mystery. I agree w/ Fashionista100 and think he's probably not entitled to call himself "Prince." Maybe someone might recognize that painting they showed? My best guess is he's a descendant of Prince Valdemar, youngest son of Christian IX. The guy in the bust and portrait looks like Christian. Christian IX of Denmark - Wikipedia, the free encyclopedia
Also, they mention he's related to the Houses of France and Spain, i.e. Bourbon, and Valdemar's wife was a Bourbon, Marie of Orleans.