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Risk-sensitive Ramsey Growth Model
Sladký, Karel
In this note we focus attention on risk-sensitive approach to an extended version of the Ramsey growth model. In contrast to the standard Ramsey model we assume that every splitting of production between consumption and capital accumulation is in uenced by some random factor governed by transition probabilities depending on the current value of the accumulated capital and possibly on some (costly) decisions. Moreover, we assume that also some additional (expensive) interventions of the decision maker are possible for changing the depreciation rate of the capital. Finding optimal policy of the extended model can be then formulated as nding optimal policy of a highly structured Markov decision process. Unfortunately usual optimization criteria for Markov decision processes cannot re ect variability-risk features of the problem. To this end, we indicate how nding policies yielding maximal risksensitive rewards.
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Ramseův růstový model za neurčitosti
Sladký, Karel
We consider an extended version of the Ramsey growth model under stochastic uncertaity modelled by Markov processes. In contrast to the standard model we assume that splitting of production between consumption and capital accumulation is influenced by some random factor, e.g. governed by transition probabilities depending on the current value of the accumulated capital, along with possible interventions of the decision maker. Basic properties of the standation formulation are summarized and compared with their counterpart in the extended version. Finding optimal policy of the extended model can be either performed by additional compensation of the (random) disturbances or can be also formulated as finding optimal control of a Markov decision process.
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Ramseův růstový model: zobecnění a algoritmická řešení
Sladký, Karel
We consider in discrete-time finite state approximations of an extended Ramsey type model under stochastic uncertainty. Recalling standard procedure of stochastic dynamic programming we present explicit formulas for finding maximum global utility of the consumers (i.e. sum of total discounted instantaneous utilities) in the approximated model along with error bounds of the approximations.
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Aproximace ve stochastických růstových modelech
Sladký, Karel
In this note, we consider finite state approximations of the stochastic Ramsey type model in discrete-time version. Recalling standard procedures of stochastic dynamic programming we present explicit formulas for finding maximum global utility of the consumers (i.e. sum of total discounted instantaneous utilies) in the approximated model.
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Optimalita prumerne variance v markovskych rozhodovacich procesech
Sladký, Karel ; Sitař, Milan
In this note, we consider discrete-time Markov decision processes with finite state space. Recalling explicit formulas for the growth rate of expected value and variance of the cumulative (random) reward, algorithmic procedures for finding optimal policies with respect to various mean variance optimality criteria are discussed. Computational experience with large scale numerical examples is reported.
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Model malé otevřené ekonomiky a možnost komplexnějšího dynamického chování
Kodera, J. ; Sladký, Karel ; Vošvrda, Miloslav
The purpose of this paper is study a three-equation dynamic model. The first equation describes commodity market. The second one demonstrates the dynamics of money market and the third equation is the interest rate parity. The task is to investigate the conditions of more complex behaviour of the model and its dependence on the money stock. The more complex dynamic behaviour, i.e., limit cycle, could appear by adding nonlinear perturbations in the investment demand function.
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