Topics in Mathematics for economics 1
First half of the course: Introduction to dynamic programming in discrete time with certainty.
Review of some basic results from elementary mathematical analysis: the set of extended real number, sup and inf in R , sequences in R, series in R, limsup and liminf for sequences.
Principle of optimality, the value function.
Properties of solutions and value function, necessary conditions for solutions, Euler equations with applications. Euler dynamics.
Second half of the course. Introduction to the theory of stochastic control in discrete time with some applications to economic and financial basic problems. The second half is divided in three parts, each one consisting (approximately) of four lectures. Part I) Introduction to the basic concepts of probability theory. Part II) Formulation of stochastic control problems and description of the dynamic programming method in discrete time. Part III) Solution of specific examples.
Bertsekas, D., (2016), Dynamic Programming and Stochastic Control, Academic Press, 1976.
Federico S., (2016) Introduction to dynamic programming in discrete time under uncertainty, Class Notes.
Villanacci, A., (2016), Introduction to dynamic programming in discrete time with certainty, Class Notes.