Jost founded the French media company Taplanete in 2003. The company published Internet sites for television shows and music and was purchased by AlloCiné in 2004. Jost later founded the website MyGayTrip which has been referred to as a TripAdvisor type site for the LGBT community. It was founded as a joint venture along with Marc Dedonder and the French magazine Têtu.
Jost founded misterbnb after a trip to Barcelona. He rented a room in a shared apartment and upon arrival was treated badly by the owner who was not expecting a gay couple. Jost felt uncomfortable by the experience and returned to Paris the next day. He then began building the site as a way for people to travel to welcoming environments. The website started as a combination MyGayTrip and short-term apartment rental service, Sejourning and has developed into an Airbnb for the LGBT community.