This paper deals with Markov Control Processes (MCPs) on Euclidean spaces with an infinite horizon and a discounted total cost. Firstly, MCPs which result from the deterministic controlled systems will be analyzed. For such MCPs, conditions that permit to establish the equation known in the literature of Economy as Euler’s Equation (EE) will be given. There will be also presented an example of a Markov Control Process with deterministic controlled system where, to obtain the optimal value function,...
In this paper a problem of consumption and investment is presented as a model of a discounted Markov decision process with discrete-time. In this problem, it is assumed that the wealth is affected by a production function. This assumption gives the investor a chance to increase his wealth before the investment. For the solution of the problem there is established a suitable version of the Euler Equation (EE) which characterizes its optimal policy completely, that is, there are provided conditions...
This work is concerned with discrete-time Markov stopping games with two players. At each decision time player II can stop the game paying a terminal reward to player I, or can let the system to continue its evolution. In this latter case player I applies an action affecting the transitions and entitling him to receive a running reward from player II. It is supposed that player I has a no-null and constant risk-sensitivity coefficient, and that player II tries to minimize the utility of player I....
This paper is related to Markov Decision Processes. The optimal control problem is to minimize the expected total discounted cost, with a non-constant discount factor. The discount factor is time-varying and it could depend on the state and the action. Furthermore, it is considered that the horizon of the optimization problem is given by a discrete random variable, that is, a random horizon is assumed. Under general conditions on Markov control model, using the dynamic programming approach, an optimality...
The paper concerns Markov decision processes (MDPs) with both the state and the decision spaces being finite and with the total reward as the objective function. For such a kind of MDPs, the authors assume that the reward function is of a fuzzy type. Specifically, this fuzzy reward function is of a suitable trapezoidal shape which is a function of a standard non-fuzzy reward. The fuzzy control problem consists of determining a control policy that maximizes the fuzzy expected total reward, where...
The article presents an extension of the theory of standard Markov decision processes on discrete spaces and with the average cost as the objective function which permits to take into account a fuzzy average cost of a trapezoidal type. In this context, the fuzzy optimal control problem is considered with respect to two cases: the max-order of the fuzzy numbers and the average ranking order of the trapezoidal fuzzy numbers. Each of these cases extends the standard optimal control problem, and for...
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