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 ([Barucci and Gozzi, 1998],...

The motivation of this paper is to prove verification theorems for stochastic optimal control of finite dimensional diffusion processes without control in the diffusion term, in the case where the value function is assumed to be continuous in time and once differentiable in the space variable...

This paper is devoted to presenting a method of proving verification theorems for stochastic optimal control of finite dimensional diffusion processes without control in the diffusion term. The value function is assumed to be continuous in time and once differentiable in the space variable...

We reconsider the optimal population size problem in a continuous time economy populated by homogenous cohorts with a fixed life span. Linear production functions in the labor input and standard rearing costs are also considered. First, we study under which conditions the successive cohorts will...

We investigate optimal consumption policies in the liquidity risk model introduced in Pham and Tankov (2007). Our main result is to derive smoothness results for the value functions of the portfolio/consumption choice problem. As an important consequence, we can prove the existence of the...

We reconsider the optimal population size problem in a continuous time economy populated by homogenous cohorts with a fixed life span. This assumption is combined with a linear production function in the labor input and standard rearing costs. A general social welfare function is specified,...

We study the compatibility of the optimal population size concepts produced by different social welfare functions and egalitarism meant as "equal consumption for all individuals of all generations". Social welfare functions are parameterized by an altruism parameter generating the Benthamite and...

We consider a utility maximization problem for an investment-consumption portfolio when the current utility depends also on the wealth process. Such kind of problems arise, e.g., in portfolio optimization with random horizon or with random trading times. To overcome the difficulties of the...

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])...