We introduce stochastic income into the standard exponential discounting model and study dependence of effective discount rates on the type of the underlying stochastic process and agent's current income level. If the income follows a process with i.i.d. increments effective discounting is...

We give short proofs of general theorems about optimal entry and exit problems in Levy models, when payoff streams may have discontinuities and be non-monotone. As applications, we consider exit and entry problems in the theory of real options, and an entry problem with an embedded option to exit.