Hunting for Superstars

An investor faces a sequence of high-risk investment opportunities. The investor ranks the corresponding projects seen so far and must immediately decide whether and how much to invest into the currently observed opportunity. Returns are realized at the end of the investment horizon, where only a small number of superstars, that is top ranked projects, generate positive returns. The payoffs of all other opportunities are zero. Under these assumptions we derive the value functions and optimal investment rules for risk-neutral or risk averse investors. As well, we obtain a few results on the comparative statics of these investment problems. A simulation study is performed for risk-neutral and risk-averse investors