We study several aspects of the dynamic programming approach to optimal control of abstract evolution equations, including a class of semilinear partial differential equations. We introduce and prove a verification theorem which provides a sufficient condition for optimality. Moreover we prove...

This paper presents a simple model in which the learning behavior of agents generates fluctuations in money demand and possibly causes a prolonged depression. We consider a stochastic Money-in-Utility model, where agents receive utility from holding money only when a liquidity shock (e.g., a...

This paper constructs a model that describes inflation cycles and prolonged depression as generated by the learning behavior of households who face a random liquidity shock in which money is needed. Households update the subjective probability of the shock based on the observation and change...

We solve analytically the Merton's problem of an investor with time additive power utility. For general state dynamics, we prove existence of two power series representations of the relevant optimal policies and value functions, which hold for all admissible risk aversion parameters. We...

In this paper we analyse a stochastic volatility model that is an extension of the traditional Black-Scholes one. We price European options on several assets by using a superstrategy approach. We characterize the Markov superstrategies, and show that they are linked to a nonlinear PDE, called...

The Dynamic Programming approach for a family of optimal investment models with vintage capital is here developed. The problem falls into the class of infinite horizon optimal control problems of PDE's with age structure that have been studied in various papers (see e.g. [11, 12], [30, 32])...