Social discount rate: spaces for agreement

We study the problem of aggregating discounted utility preferences into a social discounted utility preference model. We use an axiom capturing a social responsibility of individuals’ attitudes to time, called consensus Pareto. We show that this axiom can provide consistent foundations for welfare judgments. Moreover, in conjunction with the standard axioms of anonymity and continuity, consensus Pareto can help adjudicate some fundamental issues related to the choice of the social discount rate: the society selects the rate through a generalized median voter scheme.

Discounting and life cycle assessment: a distorting measure in assessments, a reasonable instrument for decisions

Although the weighting of environmental impacts against each other is well established in life cycle assessment practice, the weighting of impacts occurring at different points in time is still controversial. This temporal weighting is also known as discounting, which due to its potential to offend principles of intergenerational equity, is often rejected or regarded as unethical. In our literature review, we found multiple disputes regarding the comprehension of discounting. We structured those controversial issues and compared them to the original discounted utility model on which discounting is based. We explain the original theory as an intertemporal decision instrument based on future utility. We conclude that intertemporal equity controversies can be solved if discounting is applied as an individual decision instrument, rather than as an information instrument, which could underestimate environmental damages handed to future generations. Each choice related to discounting—including whether or not to discount, or to discount at a rate of zero—should be well-founded. We illustrate environmental decision-related problems as a multidimensional issue, with at least three dimensions including the type of impact and spatial and temporal distributions. Through discounting framed as a decision instrument, these dimensions can be condensed into an explicit result, from which we can draw analogies to both weighting in life cycle assessment and financial decision instruments. We suggest avoiding discounting in environmental information instruments, such as single-product life cycle assessments, footprints, or labels. However, if alternatives have to be compared, discounting should be applied to support intertemporal decisions and generate meaningful results.

Intertemporal Optimization Model of Entrepreneurs Behavior

The intertemporal problem of consumer’s behavior is the basis of modern models. The interest in this kind of problems is determined by the attempt to widen the range of directions within which it is possible to conduct additional mathematical research in the theory of consumption. The article considers the problem of maximizing discounted utility derived from an entrepreneur’s consumption due to optimal allocation of monetary means which he gets as profit from his production company and interest on assets. The difference of this problem from the basic dynamic problem of consumer’s behavior lies in the fact that an entrepreneur as an individual acts in two roles: as a consumer and as a manufacturer. Furthermore, the problem is characterized by two peculiarities: a distinctive budget limitation which includes production function and reveals an irregular differential relation and also by the presence of mixed boundary conditions on the value of capital and assets. Formalization of the problem as a dynamic optimization model is given. It was studied with the use of mathematical analysis and the means of the optimal control theory. According to parameter correlations of the model, two strategies were identified which can be recommended for an entrepreneur as the most optimal ones. The model that was developed in the course of research can serve as a tool for taking decisions because it suggests optimal strategies of allocation of financial means in an enterprise which leads to maximization of consumption utility.

Intertemporal Choice with Continuity Constraints

We consider a model of intertemporal choice where time is a continuum, the set of instantaneous outcomes (e.g., consumption bundles) is a topological space, and intertemporal plans (e.g., consumption streams) must be continuous functions of time. We assume that the agent can form preferences over plans defined on open time intervals. We axiomatically characterize the intertemporal preferences that admit a representation via discounted utility integrals. In this representation, the utility function is continuous and unique up to positive affine transformations, and the discount structure is represented by a unique Riemann–Stieltjes integral plus a unique linear functional measuring the long-run asymptotic utility.

A Q-learning Approach to a Consumption-Investment Problem

The paper deals with a discrete-time consumption investment problem with an infinite horizon. This problem is formulated as a Markov decision process with an expected total discounted utility as an objective function. This paper aims to presents a procedure to approximate the solution via machine learning, specifically, a Q-learning technique. The numerical results of the problem are provided.

A Q-learning Approach to a Consumption-Investment Problem

The paper deals with a discrete-time consumption investment problem with an infinite horizon. This problem is formulated as a Markov decision process with an expected total discounted utility as an objective function. This paper aims to presents a procedure to approximate the solution via machine learning, specifically, a Q-learning technique. The numerical results of the problem are provided.

PHASE CONSTRAINTS IN MATERIAL MEANS SEPARATION MODELS IN MICROECONOMICS

One of the important and urgent tasks of microeconomics is the problems of research of the economic system, in which there are restrictions associated with the planned volume of output or the size of the enterprise production capacity. These constraints are set by the requirement that the analyzed trajectories do not leave some given region of the control existence space. Most often, such restrictions for all time points are set in the form of inequalities, and certain requirements are imposed on the function of the phase coordinates of the object, their value at a given time. This problem is classified as an optimal control problem with mixed and phase constraints. In general, this area is of scientific interest and requires consideration. In this case, we study the microeconomic model of the household economy as the most stable object in the conditions of crises. The accumulated savings are subject to a natural phase constraint of non-negativity. This led to the study of the features of the microeconomic formulation of the problem of finding a method for the optimal division of material resources into consumed and accumulated parts, since the imposition of a natural phase restriction on the non-negativity of accumulated savings makes everything much more complicated. Just as in macroeconomics, consumption is optimized, but not in its pure form, but the integral discounted utility of consumption is maximized. The relation equation in this paper differs from a similar macroeconomic equation, since the household exists and survives in crisis conditions in a different way than do social organisms and large enterprises. That is why the article formulates and proves sufficient conditions for solving the problem with a phase constraint.

Stochastic Dynamic Programming with Non-linear Discounting

In this paper, we study a Markov decision process with a non-linear discount function and with a Borel state space. We define a recursive discounted utility, which resembles non-additive utility functions considered in a number of models in economics. Non-additivity here follows from non-linearity of the discount function. Our study is complementary to the work of Jaśkiewicz et al. (Math Oper Res 38:108–121, 2013), where also non-linear discounting is used in the stochastic setting, but the expectation of utilities aggregated on the space of all histories of the process is applied leading to a non-stationary dynamic programming model. Our aim is to prove that in the recursive discounted utility case the Bellman equation has a solution and there exists an optimal stationary policy for the problem in the infinite time horizon. Our approach includes two cases: (a) when the one-stage utility is bounded on both sides by a weight function multiplied by some positive and negative constants, and (b) when the one-stage utility is unbounded from below.

Optimal Expected Utility of Dividend Payments with Proportional Reinsurance under VaR Constraints and Stochastic Interest Rate

In this paper, we consider the problem of maximizing the expected discounted utility of dividend payments for an insurance company taking into account the time value of ruin. We assume the preference of the insurer is of the CRRA form. The discounting factor is modeled as a geometric Brownian motion. We introduce the VaR control levels for the insurer to control its loss in reinsurance strategies. By solving the corresponding Hamilton-Jacobi-Bellman equation, we obtain the value function and the corresponding optimal strategy. Finally, we provide some numerical examples to illustrate the results and analyze the VaR control levels on the optimal strategy.