This paper considers the problem of consumption and investment in a financial
market within a continuous time stochastic economy. The investor exhibits a
change in the discount rate. The investment opportunities are a stock and a
riskless account. The market coefficients and discount factor switch according
to a finite state Markov chain. The change in the discount rate leads to time
inconsistencies of the investor's decisions. The randomness in our model is
driven by a Brownian motion and a Markov chain. Following Ekeland and Pirvu we
introduce and characterize the subgame perfect strategies. Numerical
experiments show the effect of time preference on subgame perfect strategies
and the pre-commitment strategies.Comment: arXiv admin note: substantial text overlap with arXiv:1107.189