Existence and uniqueness of equilibrium in Lucas’ asset pricing model when utility is unbounded
Tóm tắt
This note presents a proof of the existence of a unique equilibrium in a Lucas (Econometrica 46(6):1429–1445, 1978) economy when the utility function displays constant relative risk aversion, and the logarithm of dividends follow a normally distributed autoregressive process of order one with positive autocorrelation. We provide restrictions on the coefficient of relative risk aversion, the discount factor and the conditional variance of the consumption process that ensure the existence of a unique equilibrium.
Tài liệu tham khảo
Alvarez, F., Stokey, N.L.: Dynamic programming with homogeneous functions. J. Econ. Theory 82(1), 167–189 (1998)
Blackwell, D.: Discounted dynamic programming. Ann. Math. Stat. 36(1), 226–235 (1965)
Boyd, J.H.: Recursive utility and the Ramsey problem. J. Econ. Theory 50(2), 326–345 (1990)
Calin, O.L., Chen, Y., Cosimano, T.F., Himonas, A.A.: Solving asset pricing models when the price-dividend function is analytic. Econometrica 73(3), 961–982 (2005)
Kamihigashi, T.: Uniqueness of asset prices in an exchange economy with unbounded utility. Econ. Theory 12(1), 103–122 (1998)
Lucas Jr., R.E.: Asset prices in an exchange economy. Econometrica 46(6), 1429–1445 (1978)
Matkowski, J., Nowak, A.S.: On discounted dynamic programming with unbounded returns. Econ. Theory 46(3), 455–474 (2011)
Ok, E.A.: Real Analysis with Economic Applications. Princeton University Press, Princeton (2007)
Martins-da Rocha, V.F., Vailakis, Y.: Existence and uniqueness of a fixed point for local contractions. Econometrica 78(3), 1127–1141 (2010)
Stachurski, J.: Economic Dynamics. MIT Press, Cambridge (2009)
Stokey, N.L., Lucas, R.E.: Recursive Methods in Economic Dynamics. Harvard University Press, Cambridge (1989)