We explore how individual risk perception influences prices and trading behavior in a market setting. Specifically, our study lets experimental participants trade assets characterized by varying shapes of return distributions. While common mean-variance models predict identical prices for most of our assets, we find trading prices to differ significantly. Assets that are perceived as being less risky on average (despite having identical volatility) trade at significantly higher prices. Individually, traders who perceive a certain asset to be less risky are also net buyers on average. With regard to different risk measures, our results show that the probability of a loss is the strongest predictor of transaction prices and risk perception. All these results hold also for experienced traders and when traders can trade two assets at the same time.