An existence theorem of intertemporal recursive utility in the presence of Lévy jumps (Q1592523)

After an introduction the assumed information structure is presented in section 2. There are two independent sources of uncertainty: a standard Brownian motion and a Lévy jump process; the motion of the state process follows a stochastic differential-difference equation. The continuous time Koopmans equation is introduced in section 3. Examples are expected discounted utility, Kreps-Portens utility, betweenness utility. Section 4 gives the existence theorem for the continuous time Koopmans equation. The theorem can also be used to prove the existence of an equilibrium asset price process.