Examining the association between delay discounting,delay aversion and physical activity in Chinese adults with type-2 diabetes mellitus

BACKGROUND The role of physical activity in diabetes is critical,influencing this disease's development,man-agement,and overall outcomes.In China,22.3%of adults do not meet the minimum level of physical activity recommended by the World Health Organization.Therefore,it is imperative to identify the factors that contributing to lack of physical activity must be identified.AIM To investigate the relationship among delay discounting,delay aversion,glycated hemoglobin(HbA1c),and various levels of physical activity in Chinese adults diagnosed with type 2 diabetes mellitus(T2DM).METHODS In 2023,400 adults with T2DM were recruited from the People's Hospital of Linxia Hui Autonomous Prefecture of Gansu Province.A face-to-face questionnaire was used to gather demographic data and details on physical activity,delay discounting,and delay aversion.In addition,HbA1c levels were measured in all 400 participants.The primary independent variables considered were delay discounting and delay aversion.The outcome variables included HbA1c levels and different intensity levels of physical activity,including walking,moderate physical activity,and vigorous physical activity.Multiple linear regression models were utilized to assess the relationship between delay discounting,delay aversion,and HbA1c levels,along with the intensity of different physical activity measured in met-hours per week.RESULTS After controlling for the sample characteristics,delay discounting was negatively associated with moderate physical activity(β=-2.386,95%CI:-4.370 to-0.401).Meanwhile,delay aversion was negatively associated with the level of moderate physical activity(β=-3.527,95%CI:-5.578 to-1.476)in the multiple linear regression model,with statistically significant differences.CONCLUSION Elevated delay discounting and increased delay aversion correlated with reduced levels of moderate physical activity.Result suggests that delay discounting and aversion may influence engagement in moderate physical activity.This study recommends that health administration and government consider delay discounting and delay aversion when formulating behavioral intervention strategies and treatment guidelines involving physical activity for patients with T2DM,which may increase participation in physical activity.This study contributes a novel perspective to the research on physical activity in adults with T2DM by examining the significance of future health considerations and the role of emotional responses to delays.

EXPECTED DISCOUNTED PENALTY FUNCTION OF ERLANG(2) RISK MODEL WITH CONSTANT INTEREST

The purpose of this paper is to consider the expected value of a discounted penalty due at ruin in the Erlang（2） risk process under constant interest force. An integro-differential equation satisfied by the expected value and a second-order differential equation for the Laplace transform of the expected value are derived. In addition, the paper will present the recursive algorithm for the joint distribution of the surplus immediately before ruin and the deficit at ruin. Finally, by the differential equation, the defective renewal equation and the explicit expression for the expected value are given in the interest-free case.

Optimal EOQ Model for Deteriorating Items Considering the Incremental Quantity Discounts and Shortages

In this present paper, a deterministic lot size model is developed for deteriorating items with incremental quantity discounts. It is assumed that shortages are permitted to occur and fully backlogged. A simple solution procedure is shown for determining the optimal order lot size and the optimal order cycle. A numerical example is used to illustrate how the solution procedure works.

Real-Time Update of Sequence Placement Logic for High Arch Dams Based on Evidence Weight Discount

Sequence placement logic plays a significant role in construction simulation of high arch dams and directly affects the simulation process and results.To establish a sequence logic for dam block placement,the construction scheme,real-time construction process,and random factors of the site all need to be considered in detail.There are few studies available currently that take all these factors into consideration.To address this problem,a real-time update of sequence placement logic for high arch dams based on evidence weight discount is proposed in this study.First,the subjective weight of the dam block sequence priority criteria is built using a consistent matrix method based on the construction scheme.Second,using evidence theory,dynamic objective weight of the priority criteria and basic probability assignment is built.Finally,using a weight self-adaptive adjustment method and comprehensive evidence discounting,the placing probabilities of different dam blocks are obtained.A case study indicates that this method can realize realtime update of sequence placement logic.

The <i>q</i>-Exponential Social Discounting Functions of Gain and Loss

Social discounting has been attracting attention in behavioral psychology, econophysics, and neuroeconomics. Several mathematical models have been proposed for social discounting;exponential discounting, hyperbolic discounting, a q-exponential discounting model based on Tsallis’ statistics. In order to experimentally examine the mathematical characteristics of the q-exponential social discounting models for gain and loss in humans, we estimated the parameters of the q-exponential social discounting models by assessing the points of subjective equality (indifference points) at seven social distances. We observed that gain was more steeply social-discounted than loss. Usefulness of the q-exponential social discounting model in social physics, econophysics, and cultural neuroeconomics are discussed.

Discrete-Time Hybrid Decision Processes: The Discounted Case

This paper is a sequel to Kageyama et al. [1], in which a Markov-type hybrid process has been constructed and the corresponding discounted total reward has been characterized by the recursive equation. The objective of this paper is to formulate a hybrid decision process and to give the existence and characterization of optimal policies.

The <i>q</i>-Exponential Probability Discounting of Gain and Loss

Probability discounting is defined as the devaluation of outcomes as the probability of receiving or paying those decreases. A q-exponential probability discounting model based on Tsallis’ statistics has been proposed in econophysics (Takahashi, 2007, Physica A). We examined (a) fitness of the models to behavioral data of probability discounting of both gain and loss;and (b) relationships between parameters in the q-exponential probability discounting model across gain and loss. Our results demonstrated that, for both gain and loss, the q-exponential model better fits the behavioral data than exponential and hyperbolic functions, and there is the sign effect in q-exponential probability discounting. Relationships between Kahneman-Tversky’s prospect theory in behavioral economics and the q-exponential probability discounting are high-lightened.

EXPECTED DISCOUNTED PENALTY FUNCTION AT RUIN FOR RISK PROCESS PERTURBED BY DIFFUSION UNDER INTEREST FORCE

In this article, the risk process perturbed by diffusion under interest force is considered, the continuity and twice continuous differentiability for Фδ（u,w） are discussed,the Feller expression and the integro-differential equation satisfied by Фδ （u ,w） are derived. Finally, the decomposition of Фδ（u,w） is discussed, and some properties of each decomposed part of Фδ（u,w） are obtained. The results can be reduced to some ones in Gerber and Landry＇s,Tsai and Willmot＇s, and Wang＇s works by letting parameter δ and （or） a be zero.

Choice of discount rate in reinforcement learning with long-delay rewards

In the world, most of the successes are results of longterm efforts. The reward of success is extremely high, but before that, a long-term investment process is required. People who are “myopic” only value short-term rewards and are unwilling to make early-stage investments, so they hardly get the ultimate success and the corresponding high rewards. Similarly, for a reinforcement learning(RL) model with long-delay rewards, the discount rate determines the strength of agent’s “farsightedness”.In order to enable the trained agent to make a chain of correct choices and succeed finally, the feasible region of the discount rate is obtained through mathematical derivation in this paper firstly. It satisfies the “farsightedness” requirement of agent. Afterwards, in order to avoid the complicated problem of solving implicit equations in the process of choosing feasible solutions,a simple method is explored and verified by theoreti cal demonstration and mathematical experiments. Then, a series of RL experiments are designed and implemented to verify the validity of theory. Finally, the model is extended from the finite process to the infinite process. The validity of the extended model is verified by theories and experiments. The whole research not only reveals the significance of the discount rate, but also provides a theoretical basis as well as a practical method for the choice of discount rate in future researches.

The Expected Discounted Tax Payments on Dual Risk Model under a Dividend Threshold

In this paper, we consider the dual risk model in which periodic taxation are paid according to a loss-carry-forward system and dividends are paid under a threshold strategy. We give an analytical approach to derive the expression of gδ(u) (i.e. the Laplace transform of the first upper exit time). We discuss the expected discounted tax payments for this model and obtain its corresponding integro-differential equations. Finally, for Erlang (2) inter-innovation distribution, closedform expressions for the expected discounted tax payments are given.

Stability Estimation for Markov Control Processes with Discounted Cost

This article explores controllable Borel spaces, stationary, homogeneous Markov processes, discrete time with infinite horizon, with bounded cost functions and using the expected total discounted cost criterion. The problem of the estimation of stability for this type of process is set. The central objective is to obtain a bounded stability index expressed in terms of the Lévy-Prokhorov metric;likewise, sufficient conditions are provided for the existence of such inequalities.

Discount rate and research progress in economic analysis on climate change

This paper has organized and summarized the economic analysis on climate change from five angles,namely,connotation of discount rate,identification of and dispute about discount rate,discounting way,impact of the discount rate,and the integrated evaluation model of climate change impact and the discount evaluation.As the climate change economic analysis shows,there is a major dispute about discount rate between the market school and the ethic school.Rate of discount largely relates to the present value of potential loss attributable to climate change,and then influences the selection of policies for adapting and slowing down climate change.In the past,the constant index discount was adopted as the main way.But with the full understanding of discount rate,the uncertainty of loss attributable to climate change has been considered in the discount.

Could we remain simply applying discount rate to evaluate the life quality of our future generations?

When we try to estimate future environmental costs resulting from our current economic activities,we usually calculate the present value of the consequences for our future generations by utilizing a discount rate as a standard economic procedure.The popularity of this procedure is solely supported by its simplicity which assumes:(1)a perfect financial market over even 100 years,and(2)existence of a stable time preference between two consecutive periods for an individual consumer.An apparent deficiency of this approach is that the present value of life quality of future generations varies to a large extent along an arbitrarily chosen discount rate.As a matter of fact,the discount rate,which could reflect the time preference as2%or 5%,matters when we predict current strategies of environmental protection for future generations.Simply applying a discount rate to evaluate the quality of our future generation,without clarifying the actual production mechanism behind this,is almost to the same as ignoring the fact that all of the goods are produced through an actual production process and that environmental degradation reduces the efficiency of that process.The greatest concern for our future generations should not be given by an assumed discount rate,since the discount rate itself is determined by financial market conditions at certain points in time.

Technology advance and discounting of the historical emission responsibilities

Solving the dispute over historical greenhouse gases emission responsibility is critical for the future climate agreement.This article borrows the methodology from the carbon budget proposal,but further develops this approach by proposing discount of the historical responsibility due to the technology advance.Firstly,it studies the Annex I countries'mitigation and financial responsibilities of the historical emission in the carbon budget proposal;furthermore,it analyzes the results and implications of the discount approach.Results show that the discount method significantly reduces the burden of the mitigation and financial responsibilities of the Annex I countries.Thus,we claim that the discount approach is a systematic,pragmatic,and fair approach to solve the historical responsibility dispute and financial problems for the post-2020international climate institutions.

Quantity discount contracts for supply chain coordination under asymmetric information and disruptions

The quantity discount contracts are investigated for a one-supplier-one-retailer supply chain with asymmetric information when the retailer's cost is disrupted. While the retailer's cost structure is asymmetric information, two all-unit quantity discount contract models, fixed expected-profit percentage discount(FEPD) and fixed wholesale-pricing percentage discount(FWPD) under asymmetric information are proposed in a regular scenario. When the retailer's cost distribution fluctuates due to disruptions, the optimal emergency strategies of supply chains are obtained under asymmetric information. Using numerical methods, the impact of cost disruptions on decisions about the regular wholesale price, discount wholesale price, order quantity and expected profits of the retailer, the supplier as well as the total system are analyzed. It is found that the FEPD policy is more robust and adaptable than the FWPD policy in disruption circumstances.

The Impact of Discount Rate and Price on Intertemporal Groundwater Models in Southwest Kansas

Agriculture plays a vital role in the growth and development of the High Plains Region of the United States. With the development and adoption of irrigation technology, this region was transformed into one of the most agriculturally productive regions in the world [1]. The primary source of irrigation in this region is the Ogallala Aquifer. Currently, water from the aquifer is being used at a much faster rate than natural recharge can occur, resulting in a high rate of depletion from this finite resource. Depletion of scarce water resources will have a significant economic impact on the long-term sustainability of the region. The objective of this study is to evaluate the impact alternative prices and discount rates have on groundwater policy recommendations. Deterministic models of groundwater withdrawals were developed and used in order to analyze and evaluate the impact of high, average, and low crop prices in a status quo scenario as well as a policy scenario reducing irrigated acreage allocation. Furthermore, this study analyzes the effects and associated consequences of alternative discount rates on net and total revenue. As indicated by results of this study, alternative prices, costs, and discount rates utilized in a model have an effect on policy effectiveness.

Asymptotics of discounted aggregate claims for renewal risk model with risky investment

Under the assumption that the claim size is subexponentially distributed and the insurance surplus is totally invested in risky asset, a simple asymptotic relation of tail probability of discounted aggregate claims for renewal risk model within finite horizon is obtained. The result extends the corresponding conclusions of related references.

Production Decision Based on Discounted Price and Delivery Frequency for Garment Original Equipment Manufacturer with Constrained Capacity

Original equipment manufacturers(OEM) have never been so important and powerful as it is today in garment manufacturing industry.The OEMsupplier's production decisions always have a great impact on the market performance and the profits of a garment brand manufacturer.With constrained capacity and multiply buyers,howto make reasonable production decisions is an urgent problem for OEMsuppliers.A price discount model with a single OEMsupplier and two buyers is proposed to deal with the problem.Based on this model,the OEMsupplier could satisfy buyers' demands and guarantee their profits as well through adjusting price and delivery frequency.A numerical example validates the validity of the model.

Study of the Discount on Private Placements and Risk of Stock Market Crash in Listed Companies

With the gradual completion of the split-share structure reform,private placement has gradually become the mainstream of refinancing. One of the points that the practical and theoretical circles are widely concerned about is that the private placement price is often higher than the market price at the time of the private placement. High discounts are often accompanied by the transmission of benefits,and the increase in insider information will lead to the risk of a stock market crash? This paper intends to use the data of A-share listed companies from 2006 to 2015 to empirically study the relationship between the discount on private placements and the risk of stock market crash. At the same time,this paper examines whether the degree of information asymmetry plays a regulatory role in the relationship between the discount on private placements and the risk of stock market crash. This paper provides a certain reference for the regulatory authorities to improve the relevant laws and regulations in the private placement,and to provide a certain reference for the protection of the interests of small and medium-sized investors.

Moments of Discounted Dividend Payments in the Sparre Andersen Model with a Constant Dividend Barrier

We consider the Sparre Andersen risk process in the presence of a constant dividend barrier, and propose a new expected discounted penalty function which is different from that of Gerber and Shiu. We find that iteration mothed can be used to compute the values of expected discounted dividends until ruin and the new penalty function. Applying the new function and the recursion method proposed in Section 5, we obtain the arbitrary moments of discounted dividend payments until ruin.