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Form of the utility function
In economics and finance, exponential utility is a specific form of the utility function, used in some contexts because of its convenience when risk (sometimes
Exponential_utility
Concept in economics and decision theory
alternative utility functions such as: CES (constant elasticity of substitution). Isoelastic utility Exponential utility Quasilinear utility Homothetic
Utility
Concept in economics
aversion. Isoelastic function Constant elasticity of substitution Exponential utility Risk aversion Ljungqvist, Lars; Sargent, Thomas J. (2000). Recursive
Isoelastic_utility
measure which depends on the risk aversion of the user through the exponential utility function. It is a possible alternative to other risk measures as
Entropic_risk_measure
Problem of allocation of money by consumers in order to most benefit themselves
In microeconomic theory, the utility maximization problem formalizes how a consumer allocates limited resources across different goods and services. The
Utility_maximization_problem
value of the utility function. Notable special cases of HARA utility functions include the quadratic utility function, the exponential utility function,
Hyperbolic absolute risk aversion
Hyperbolic_absolute_risk_aversion
Return on investment metrics
with quadratic utility, (2) two-periods, exponential utility, and normally-distributed returns, (3) infinite-periods, quadratic utility, and stochastic
Consumption-based capital asset pricing model
Consumption-based_capital_asset_pricing_model
Economics theory
do not change it. The following expressions relate to this term: Exponential utility of the form u ( c ) = 1 − e − α c {\displaystyle u(c)=1-e^{-\alpha
Risk_aversion
Discount function in which future returns are weighted exponentially
over time (with or without uncertainty). Formally, exponential discounting occurs when total utility is given by U ( { c t } t = t 1 t 2 ) = ∑ t = t 1
Exponential_discounting
Topics referred to by the same term
risk aversion, a term in Economics referring to a property of the exponential utility function Control of Alien Refugees Act 1960 in Uganda. Cara Sucia
Cara
a way to design the queries such that, for power-log utilities and negative-exponential utilities, the predictions do not depend on canceling subjective
Utility_assessment
Theorem in portfolio theory
risk aversion (HARA) (including the power utility function, logarithmic function and the exponential utility function), separation theorems can be obtained
Mutual fund separation theorem
Mutual_fund_separation_theorem
investor's remaining lifetime. Under certain assumptions including exponential utility and a single asset with returns following an ARMA(1,1) process, a
Intertemporal portfolio choice
Intertemporal_portfolio_choice
Concept in financial economics
convex risk measure which is not coherent. It is related to the exponential utility. The superhedging price is a coherent risk measure. In a situation
Coherent_risk_measure
even in the bipartite case, the number of stable marriages might be exponential in the number of agents. In the bipartite case, the Gale–Shapley algorithm
Optimal_stable_matching
Increase in utility with network size
assertion of David P. Reed that the utility of large networks, particularly social networks, can scale exponentially with the size of the network. The reason
Reed's_law
Growth at a rate that is a logarithmic function
multiplying by a fixed constant. Logarithmic growth is the inverse of exponential growth and is very slow. A familiar example of logarithmic growth is
Logarithmic_growth
Hypothetical event
mistake the logistic function (S-function) for an exponential function, and to see a "knee" in an exponential function where there can in fact be no such thing
Technological_singularity
American financial economist (born 1946)
2006). "Equilibrium asset pricing: with non-Gaussian factors and exponential utilities". Quantitative Finance. 6 (6): 455–463. doi:10.1080/14697680600804437
Dilip_Madan
Economic theory
theories such as the concept of exponential growth. It is commonly understood that growth will not continue to rise exponentially, rather it is subject to different
Diminishing_returns
X}\right]\leq 1\}} where u ( X ) {\displaystyle u(X)} is the exponential utility function. Artzner, Philippe; Delbaen, Freddy; Eber, Jean-Marc; Heath
Acceptance_set
Base-16 numeric representation
floating-point standard). Just as decimal numbers can be represented in exponential notation, so too can hex numbers. P notation uses the letter P (or p
Hexadecimal
Legal concept regulating rights of a creative work
the advent of copyright, 6th century to 18th century. Blue shows printed books. Log-lin plot; a straight line therefore shows an exponential increase.
Copyright
Hypothetical end-of-the-world scenario
(1986). In Chapter 4, Engines Of Abundance, Drexler illustrates both exponential growth and inherent limits (not gray goo) by describing "dry" nanomachines
Gray_goo
Difference in valuation of a payoff when receiving it earlier versus later
to explain intertemporal preferences. Exponential discounted utility was first described in the discounted utility model. The equation is as follows: U
Time_preference
Economic model which weighs rewards based on when they are received
this integral exists. Exponential discounting and hyperbolic discounting are the two most commonly used examples. Discounted utility Intertemporal choice
Discount_function
Probability distribution
distribution function of an exponential distribution with rate α. Pareto distribution can be constructed by hierarchical exponential distributions. Let ϕ |
Pareto_distribution
Economics concept
the financial world, this process is normally modeled in the form of exponential discounting, a time-consistent model of discounting. Many psychological
Hyperbolic_discounting
Family of functions to transform data
to 1. Q-exponential family – a generalization of the standard exponential family that replaces the exponential function with the q-exponential form derived
Power_transform
Free online crowdsourced encyclopedia
domain from wikipedia.com to wikipedia.org. After an early period of exponential growth, the growth rate of the English Wikipedia in terms of the numbers
Wikipedia
Increasing value with increasing participation
telephone. This created more value and utility due to the increase in users. Eventually, increased usage through exponential growth led to the telephone being
Network_effect
Branch of mathematics
representing large games with limited interaction patterns, as it can exponentially reduce the amount of information needed to fully describe the game.
Graphical_game_theory
Software update distribution service for Microsoft Windows
number of complaints about this issue in September 2013. The cause was an exponential algorithm in the evaluation of superseded updates, which had grown large
Windows_Update
Burst of electromagnetic energy
building up quickly to their maximum level. The classic model is a double-exponential curve which climbs steeply, quickly reaches a peak and then decays more
Electromagnetic_pulse
books before the advent of copyright, 500s to 1700s. Blue shows printed books. Log-lin plot; a straight line therefore shows an exponential increase.
History_of_copyright
Type of denial-of-service software attack
own copy of the same infinite loop. This has the effect of causing an exponential growth in processes. As modern Unix systems generally use a copy-on-write
Fork_bomb
Infinite sum of monomials
is one of the most important examples of a power series, as are the exponential function formula e x = ∑ n = 0 ∞ x n n ! = 1 + x + x 2 2 ! + x 3 3 !
Power_series
When a decision-maker's future preferences can contradict earlier preferences
that decision-makers are exponential discounters. Exponential discounting posits that the decision maker assigns future utility of any good according to
Dynamic_inconsistency
Paradox involving a game with repeated coin flipping
explicit introduction of a utility function, an expected utility hypothesis, and the presumption of diminishing marginal utility of money. According to Daniel
St._Petersburg_paradox
American infrastructure services corporation
power in over 20 million sq. ft. of data centers. It was experiencing exponential growth with the onset of artificial intelligence. Cupertino Electric
Quanta_Services
Experimental design framework
designing an experiment is to maximize the expected utility of the experiment outcome. The utility is most commonly defined in terms of a measure of the
Bayesian_experimental_design
Mathematical function for the probability a given outcome occurs in an experiment
For example, suppose we want to generate a random variable having an exponential distribution with parameter λ {\displaystyle \lambda } — that is, with
Probability_distribution
Visual representation of a decision-making problem
becoming an alternative to the decision tree which typically suffers from exponential growth in number of branches with each variable modeled. ID is directly
Influence_diagram
Number measuring the chance an event occurs
and stated that the frequency of an error could be expressed as an exponential function of the numerical magnitude of the error – disregarding sign
Probability
Task manager program found in many Unix-like operating systems
The instant variations of the number of processes are damped with an exponential decay formula which is calculated using fixed point math. The ps program
Top_(software)
Book by Richard Dawkins
misguided, as the numbers of ancestors and descendants seem to grow exponentially as generations are added to the lineage tree. In just 80 generations
River_Out_of_Eden
Family of continuous probability distributions
(t\mu ,t\lambda ).} The inverse Gaussian distribution is a two-parameter exponential family with natural parameters − λ / ( 2 μ 2 ) {\displaystyle -\lambda
Inverse_Gaussian_distribution
Instructions for the x86 microprocessors
vectorized, supported by Knights Landing AVX-512 Exponential and Reciprocal Instructions (ER) – exponential and reciprocal operations designed to help implement
Advanced_Vector_Extensions
Sequence of characters that forms a search pattern
regular language. They came into common use with Unix text-processing utilities. Different syntaxes for writing regular expressions have existed since
Regular_expression
Stress-relieving toy
angular momentum. Over time, the speed of rotation decreases following an exponential decay pattern, meaning that while it slows gradually, it cannot spin
Fidget_spinner
Resource problem in machine learning
Urvoy, Tanguy; Clérot, Fabrice (2015), "A Relative Exponential Weighing Algorithm for Adversarial Utility-based Dueling Bandits" (PDF), Proceedings of the
Multi-armed_bandit
Opposite of a probability event
Probability distribution Bernoulli distribution Binomial distribution Exponential distribution Normal distribution Pareto distribution Poisson distribution
Complementary_event
Mathematical model which is both linear and time-invariant
eigenfunctions, and the basis functions of the transforms, are complex exponentials. As a result, if the input to a system is the complex waveform A s e
Linear_time-invariant_system
Interpretation of probability
every Bayesian procedure is admissible. Following the work on expected utility theory of Ramsey and von Neumann, decision-theorists have accounted for
Bayesian_probability
Assembly of photovoltaic cells used to generate electricity
solar cell. Falling costs have been the biggest factor in the recent exponential growth of Solar energy. Since 2010, the cost of solar photovoltaic electricity
Solar_panel
Mathematical relation assigning a probability event to a cost
specific domains, variously called a reward function, a profit function, a utility function, a fitness function, etc.), in which case it is to be maximized
Loss_function
Topics referred to by the same term
of Edison International, a California public utility holding company Ei(x) may refer to the Exponential integral. This disambiguation page lists articles
Eix_(disambiguation)
Systematic approach to estimating the strengths and weaknesses of alternatives
Dupuit began to look at the utility users would gain from the project. He determined that the best method of measuring utility is by learning one's willingness
Cost–benefit_analysis
Toronto, Canada. After the end of World War II, electric demand grew exponentially. Toronto Hydro built house-shaped substations with slight variations
List of fake buildings in Toronto
List_of_fake_buildings_in_Toronto
Self-report mood disorder questionnaire
revealed that the total score distribution on the PHQ-9 approximates an exponential pattern in the general population.. The PHQ-2 is a shortened version
PHQ-9
Japanese stock market index
sharply from the textbook model of stock averages, which grow at a steady exponential rate. During the Japanese asset price bubble, the average hit its bubble-era
Nikkei_225
Part of an electrical transmission and distribution system
as switchyards. Substations may be owned and operated by an electrical utility, or may be owned by a large industrial or commercial customer. Generally
Substation
Topics referred to by the same term
used to define fractal dimensions Topological entropy, a measure of exponential growth in dynamical systems; equivalent to the rate of increase of α->0
Entropy_(disambiguation)
Psychological theory of motivation
approaching deadlines, arguing that the perceived utility of a given activity increases exponentially as the deadline nears. These and similar ideas have
Temporal_motivation_theory
Analogue synthesizer
to the more standardized ADSR). The attack and decay stages are both exponential curves, with the attack being inverted. The ASR envelope's has two knobs
Volca_Modular
Economic theory
the worker is either dismissed or kept employed during the time. The exponential function appears, because the occasion of dismiss in the interval is
Shapiro–Stiglitz_theory
Methods of safely sharing general data
carefully calibrated noise into statistical computations such that the utility of the statistic is preserved while provably limiting what can be inferred
Differential_privacy
Mathematical statistics distance measure
squared distance, and for certain classes of distributions (notably an exponential family), it satisfies a generalized Pythagorean theorem (which applies
Kullback–Leibler_divergence
Algorithm trading more space for lower time
in cryptography, where the adversary is trying to do better than the exponential time required for a brute-force attack. Rainbow tables use partially
Space–time_tradeoff
Metropolis in Chhattisgarh, India
a major commercial hub for trade and commerce in the region. It has exponential industrial growth and has become a major business hub in Central India
Raipur
Process of using data analysis for predicting population data from sample data
low-dimensional models with log-concave likelihoods (such as with one-parameter exponential families). For a given dataset that was produced by a randomization design
Statistical_inference
Data storage technology
failing within one hour was four times larger than predicted by the exponential statistical distribution—which characterizes processes in which events
RAID
British Labour Party politician
also a non-executive chairman of the quantum technology company Quantum Exponential. "Ian Pearson". Thames Water. Retrieved 16 July 2025. "Who we are". EQTEC
Ian_Pearson
freedom and enjoyment. The tourism industry in the U.S. experienced exponential growth as tourists could travel almost anywhere with a fast, reliable
Tourism_in_the_United_States
Intelligence of machines
problems because they experience a "combinatorial explosion": They become exponentially slower as the problems grow. Even humans rarely use the step-by-step
Artificial_intelligence
Probability distribution of energy states of a system
where pi is the probability of the system being in state i, exp is the exponential function, εi is the energy of that state, and a constant kBT of the distribution
Boltzmann_distribution
Type of electronic frequency mixer
logarithm of the associated differential (X) input current so that the exponential characteristics of the following transistors result in an ideally perfect
Gilbert_cell
Management system for electrical power distribution
11747849B2 In recent years, utilization of electrical energy increased exponentially and customer requirement and quality definitions of power were changed
Distribution management system
Distribution_management_system
Statistical model for a binary dependent variable
by some value of the predictor. base e {\displaystyle e} denotes the exponential function. The odds of the dependent variable equaling a case (given some
Logistic_regression
System information, diagnostics, and auditing program
precision calculations. Uses x87 instructions intended for trigonometric and exponential functions. The program has 4 editions: Extreme — diagnostics, testing
AIDA64
Model Utility Branches Exponential integrate-and-fire Describes compact and computationally efficient nonlinear spiking neuron models with one or two variables
List of research methods in biology
List_of_research_methods_in_biology
2024 wildfire in Texas and Oklahoma, USA
County Road O. The cause of the fire was downed power lines due to a broken utility pole. InciWeb records an ignition time of approximately 2:20 p.m. CST,
Smokehouse_Creek_Fire
Statistical relationship
relationship that can be exploited in practice. For example, an electrical utility may produce less power on a mild day based on the correlation between electricity
Correlation
Period of rapid progress in AI
Google's Gemini. The popularity of text-to-video generative AI tools grew exponentially. With the release of models such as OpenAI's Sora in 2024, the use of
AI_boom
Operations research that evaluates multiple conflicting criteria in decision making
also known as multi-attribute decision making (MADM), multiple attribute utility theory, multiple attribute value theory, multiple attribute preference
Multiple-criteria decision analysis
Multiple-criteria_decision_analysis
factor analysis Exponential dispersion model Exponential distribution Exponential family Exponential-logarithmic distribution Exponential power distribution –
List_of_statistics_articles
Arbitrary-precision calculator supporting interactive and scripted use
functions for calculating sine, cosine, arctangent, natural logarithm, the exponential function and the two parameter Bessel function J. Most standard mathematical
Bc_(programming_language)
List of companies which use multi-level marketing
Touchstone Crystal Tastefully Simple Telecom Plus and its main subsidiary Utility Warehouse Tupperware USANA Health Sciences Usborne Publishing Vector Marketing
List of multi-level marketing companies
List_of_multi-level_marketing_companies
U.S. Army investigations of psychic phenomena
Rice University Marks 10 years: Exploring supernatural encounters and exponential growth". KPRC-TV. Archived from the original on November 2, 2024. Clarke
Stargate Project (U.S. Army unit)
Stargate_Project_(U.S._Army_unit)
Bound on probability of a random variable being far from its mean
standard deviations around the mean, in statistics. The inequality has great utility because it can be applied to any probability distribution in which the
Chebyshev's_inequality
Hypothesized risk to human existence
intelligent than its creators would recursively improve itself at an exponentially increasing rate, too quickly for its handlers or society at large to
Existential risk from artificial intelligence
Existential_risk_from_artificial_intelligence
Statistical transform
coincides with the exponential distribution, and the equation for R2 above is a simple way of generating the required exponential variate. The polar form
Box–Muller_transform
Four-dimensional number system
q=a+b\,\mathbf {i} +c\,\mathbf {j} +d\,\mathbf {k} =a+\mathbf {v} ,} the exponential is computed as exp ( q ) = ∑ n = 0 ∞ q n n ! = e a ( cos ‖ v ‖ +
Quaternion
Theorem of convex functions
particular importance in statistical physics when the convex function is an exponential, giving: e E [ X ] ≤ E [ e X ] , {\displaystyle e^{\operatorname
Jensen's_inequality
Branch of mathematics concerning probability
Important continuous distributions include the continuous uniform, normal, exponential, gamma and beta distributions. In probability theory, there are several
Probability_theory
(such as Proportional Fair, Modified Largest Weighted Delay First, and Exponential Proportional Fair, Log and Exp rules), AMC scheme, Channel Quality Indicator
LTE-Sim
Problem optimization method
more values of fib, or subproblems, are recalculated, leading to an exponential time algorithm. Now, suppose we have a simple map object, m, which maps
Dynamic_programming
Economical computational problem
utilities are normalized to [0,1], so this is actually a multiplicative approximation: the gain cannot be more than epsilon times the highest utility
Nash_equilibrium_computation
Function acting on the space of physical states in physics
physical states onto another space of states. The simplest example of the utility of operators is the study of symmetry (which makes the concept of a group
Operator_(physics)
Fictional universe created by Iain M. Banks
of the universe allowing permanent expansion (at least assuming non-exponential growth), this frees them from having to compete for living space. The
The_Culture
EXPONENTIAL UTILITY
EXPONENTIAL UTILITY
EXPONENTIAL UTILITY
EXPONENTIAL UTILITY
Girl/Female
Tamil
Triguna | தà¯à®°à®¿à®•à¯‚நா
Maya, Illusion, Goddess Durga
Biblical
same as Aiath
Girl/Female
Arabic, Egyptian
Intelligent
Boy/Male
American, British, English, Gaelic, Scottish
Friend of the Sea; Variant of Erwin; Boar-friend; Place Name; Beautiful
Boy/Male
Hindu, Indian, Marathi
Lord of Beauty
Male
German
German form of Latin Vincentius, VINZENZ means "conquering."
Girl/Female
Hindu, Indian, Tamil
Sun and Moon
Boy/Male
Afghan, Australian
Prostrating in Prayers
Male
Spanish
Portuguese and Spanish form of Greek Dismas, DIMAS means "sunset."
Girl/Female
Biblical
Stretching.
EXPONENTIAL UTILITY
EXPONENTIAL UTILITY
EXPONENTIAL UTILITY
EXPONENTIAL UTILITY
EXPONENTIAL UTILITY
n.
The doctrine that utility is the sole standard of morality, so that the rectitude of an action is determined by its usefulness.
n.
The doctrine that virtue is founded in utility, or that virtue is defined and enforced by its tendency to promote the highest happiness of the universe.
v. t.
Yielding of service; advantage derived; capability of being used; usefulness; utility.
n.
That phase of the doctrine of utilitarianism taught by Jeremy Bentham; the doctrine that the morality of actions is estimated and determined by their utility; also, the theory that the sensibility to pleasure and the recoil from pain are the only motives which influence human desires and actions, and that these are the sufficient explanation of ethical and jural conceptions.
n.
The hard, white, opaque, fine-grained substance constituting the tusks of the elephant. It is a variety of dentine, characterized by the minuteness and close arrangement of the tubes, as also by their double flexure. It is used in manufacturing articles of ornament or utility.
n.
The quality or state of being useful; utility; serviceableness; advantage.
v. t.
To deprive of utility; to render useless.
a.
Of or pertaining to utility; consisting in utility; /iming at utility as distinguished from beauty, ornament, etc.; sometimes, reproachfully, evincing, or characterized by, a regard for utility of a lower kind, or marked by a sordid spirit; as, utilitarian narrowness; a utilitarian indifference to art.
n.
The quality or state of being useful; usefulness; production of good; profitableness to some valuable end; as, the utility of manure upon land; the utility of the sciences; the utility of medicines.
n.
Happiness; the greatest good, or happiness, of the greatest number, -- the foundation of utilitarianism.
n.
The property or aggregate properties of a thing by which it is rendered useful or desirable, or the degree of such property or sum of properties; worth; excellence; utility; importance.
a.
Pertaining to exponents; involving variable exponents; as, an exponential expression; exponential calculus; an exponential function.
n.
Adaptation to satisfy the desires or wants; intrinsic value. See Note under Value, 2.
n.
Worth estimated by any standard of purchasing power, especially by the market price, or the amount of money agreed upon as an equivalent to the utility and cost of anything.
n.
An expression of the condition of equality between two algebraic quantities or sets of quantities, the sign = being placed between them; as, a binomial equation; a quadratic equation; an algebraic equation; a transcendental equation; an exponential equation; a logarithmic equation; a differential equation, etc.