The Analysis of a Mathematical Model Associated to an Economic Growth Process Exposed to a Risk Factor

摘要

In this paper, we will analyze an endogenous economical growth model in the case of which the occurrence of a disaster is possible. This economical growth model leads to an optimal control problem with an infinite horizon. For this problem we will prove that the solution of the optimal control problem verifies Euler-Lagrange's equation, therefore providing the necessary optimal conditions for an optimal control problem. Using these necessary conditions we will determine the consumption evolution equation. Also, we will prove a necessary optimality condition in terms of value function