Could you explain that a bit more please? The paper says, "We propose a model... of people influenced by lucky or unlucky random events." So unlucky events are being considered too. But it's possible that I'm not understanding what you mean.
2. A lucky event intercepts the position of agent Ak: this means that a lucky event has occurred during the last six month; as a consequence, agent Ak doubles her capital/success with a probability proportional to her talent Tk. It will be Ck(t) = 2Ck(t − 1) only if rand[0, 1] < Tk, i.e. if the agent is smart enough to profit from his/her luck.
3. An unlucky event intercepts the position of agent Ak: this means that an unlucky event has occurred during the last six month; as a consequence, agent Ak halves her capital/success, i.e. Ck(t) = Ck(t − 1)/2.
Note that the equation for lucky events includes talent, but unlucky events do not.