infinite horizon
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2022 ◽  
Author(s):  
Alexander Shapiro ◽  
Yi Cheng

A construction of the dual of a periodical formulation of infinite-horizon linear stochastic programs with a discount factor is discussed. The dual problem is used for computing a deterministic upper bound for the optimal value of the considered multistage stochastic program. Numerical experiments demonstrate behavior of that upper bound, especially when the discount factor is close to one.


Author(s):  
Alain Jean-Marie ◽  
Mabel Tidball ◽  
Víctor Bucarey López

We consider a discrete-time, infinite-horizon dynamic game of groundwater extraction. A Water Agency charges an extraction cost to water users and controls the marginal extraction cost so that it depends not only on the level of groundwater but also on total water extraction (through a parameter [Formula: see text] that represents the degree of strategic interactions between water users) and on rainfall (through parameter [Formula: see text]). The water users are selfish and myopic, and the goal of the agency is to give them incentives so as to improve their total discounted welfare. We look at this problem in several situations. In the first situation, the parameters [Formula: see text] and [Formula: see text] are considered to be fixed over time. The first result shows that when the Water Agency is patient (the discount factor tends to 1), the optimal marginal extraction cost asks for strategic interactions between agents. The contrary holds for a discount factor near 0. In a second situation, we look at the dynamic Stackelberg game where the Agency decides at each time what cost parameter they must announce. We study theoretically and numerically the solution to this problem. Simulations illustrate the possibility that threshold policies are good candidates for optimal policies.


Author(s):  
Jeremy Kettering ◽  
Asen Kochov

Suppose the consumption space is discrete. Our first contribution is a technical result showing that any continuous utility function of any stationary preference relation over infinite consumption streams has convex range, provided that the agent is sufficiently patient. Putting the result to use, we consider a model of endogenous discounting (a generalization of the standard model with geometric discounting) and show the uniqueness of the consumption-dependent discount factor as well as the cardinal uniqueness of utility. Comparative statics are then provided to substantiate the uniqueness. For instance, we show that, as in the more familiar case of an infinitely divisible good, the cardinal uniqueness of utility captures an agent’s desire to smooth consumption over time.


PAMM ◽  
2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Timm Faulwasser ◽  
Christopher M. Kellett

2021 ◽  
pp. 162-171
Author(s):  
Margarita Kozhevnikova

The author undertakes a phenomenological analysis of research process on the example of the philosophical and anthropological study of education. In accordance with the phenomenological approach, the research process with its general methodological regularities is divided into three phases: 1) the preliminary phase of thematization; 2) the phenomenological phase itself, which opens up for the researcher his own direct experience of the subject, its obviousness; 3) the post-phenomenological phase. Within the boundaries of the last phase the tension between "experience" and "language" is resolved, that is, experience is expressed, an exit to the general life world apeears, an approach to certification is carried out. From this point of view, the problem of "reliability" and "identity" is raised, which is especially relevant for the phenomenological perspective. Certain phenomenological solutions to this problem were developed by Hegel and Husserl. Taking into account the existing solutions, three possible versions of the interpretations of the identity are considered: proceeding from objectivity; intersubjectivity; subjectivity. The application of phenomenological analysis to practical, scientific and philosophical fields of research allowed us to distinguish three levels of verification during certification. At the first level, experience, representation and concept come to the fore; at the second level – the requirement of unity of experience, representation and thinking; at the third – a certificate consisting of checking the stability of the trusted before the other / Other. The understanding of the latter has the meaning of a "dialectical movement", according to Hegel, and represents an "infinite horizon... of approximations", according to Husserl. These criteria are explained in the perspective of subjectivity, which reveals its possibilities when compared with interpretations based on the understanding of the true as objective (in particular, when compared with "scientific realists") and intersubjective.


Author(s):  
Sonam Kharade ◽  
Sarang Sutavani ◽  
Sushama Wagh ◽  
Amol Yerudkar ◽  
Carmen Del Vecchio ◽  
...  

PLoS ONE ◽  
2021 ◽  
Vol 16 (11) ◽  
pp. e0260257
Author(s):  
Leif K. Sandal ◽  
Sturla F. Kvamsdal ◽  
José M. Maroto ◽  
Manuel Morán

An infinite-horizon, multidimensional optimization problem with arbitrary yet finite periodicity in discrete time is considered. The problem can be posed as a set of coupled equations. It is shown that the problem is a special case of a more general class of contraction problems that have unique solutions. Solutions are obtained by considering a vector-valued value function and by using an iterative process. Special cases of the general class of contraction problems include the classical Bellman problem and its stochastic formulations. Thus, our approach can be viewed as an extension of the Bellman problem to the special case of nonautonomy that periodicity represents, and our approach thereby facilitates consistent and rigorous treatment of, for example, seasonality in discrete, dynamic optimization, and furthermore, certain types of dynamic games. The contraction approach is illustrated in simple examples. In the main example, which is an infinite-horizon resource management problem with a periodic price, it is found that the optimal exploitation level differs between high and low price time intervals and that the solution time paths approach a limit cycle.


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