TY - BOOK

T1 - Asymptotic behaviour of the utility vector in a dynamic programming model

AU - Zijm, W.H.M.

PY - 1980

Y1 - 1980

N2 - In mathematical economics (e.g. Leontief substitution systems) and in Markov decision theory we often deal with dynamic programming recursions of the following form
$ x(n+1) = \max_{P \in M} Px(n) ; n = 0,1,2,... $
where x(0) is assumed to be a strictly positive vector. M is a set of matrices, generated by all possible interchanges of corresponding rows, taken from a fixed finite set of nonnegative square matrices (not necessarily stochastic). We investigate the asymptotic behaviour of the vector x(n) in terms of generalized eigenvectors of a particular matrix $P ]in M$, with respect to its spectral radius $\sigma(P)$. This paper extends earlier results of Sladky [11] and Zijm [13].

AB - In mathematical economics (e.g. Leontief substitution systems) and in Markov decision theory we often deal with dynamic programming recursions of the following form
$ x(n+1) = \max_{P \in M} Px(n) ; n = 0,1,2,... $
where x(0) is assumed to be a strictly positive vector. M is a set of matrices, generated by all possible interchanges of corresponding rows, taken from a fixed finite set of nonnegative square matrices (not necessarily stochastic). We investigate the asymptotic behaviour of the vector x(n) in terms of generalized eigenvectors of a particular matrix $P ]in M$, with respect to its spectral radius $\sigma(P)$. This paper extends earlier results of Sladky [11] and Zijm [13].

M3 - Report

T3 - Memorandum COSOR

BT - Asymptotic behaviour of the utility vector in a dynamic programming model

PB - Technische Hogeschool Eindhoven

CY - Eindhoven

ER -