scholarly journals Commonotonicity and time-consistency for Lebesgue-continuous monetary utility functions

2021 ◽  
Author(s):  
Freddy Delbaen
Keyword(s):  
Time Consistency ◽  
Utility Functions ◽  
Time Step ◽  
Conditional Expectations ◽  
Probability Spaces ◽  
Monetary Utility Functions

AbstractIt is proved that monetary utility functions that are commonotonic and time-consistent are conditional expectations. We also give additional results on atomless and conditionally atomless probability spaces. These notions describe that in a filtration, there are many new events at each time step.

WEIGHTED QUASI-ARITHMETIC MEANS AND A RISK INDEX FOR STOCHASTIC ENVIRONMENTS

2011 ◽  
Vol 19 (supp01) ◽  
pp. 1-16 ◽  
Author(s):  
YUJI YOSHIDA
Keyword(s):  
Probability Density ◽  
Risk Premium ◽  
Risk Index ◽  
Utility Functions ◽  
Probability Density Functions ◽  
Density Functions ◽  
Arithmetic Means ◽  
Stochastic Environments ◽  
Order Stochastic Dominance ◽  
Conditional Expectations

In this paper, the weighted quasi-arithmetic means are discussed from the viewpoint of utility functions and downward risks in economics. Representing the weighting functions by probability density functions and the conditional expectations, an index for downward risks in stochastic environments is derived. This paper discusses the relation among the index, the first-order stochastic dominance and the risk premium in economics, and further it investigates the relation between the index and value-at-risks which are known as another estimation for downward risks in finance. Finally, this paper shows a lot of examples of the weighted quasi-arithmetic mean and the aggregated mean ratio for various typical utility functions with various typical utility functions and probability density functions.

EQUILIBRIUM PRICES FOR MONETARY UTILITY FUNCTIONS

2008 ◽  
Vol 11 (03) ◽  
pp. 325-343 ◽  
Author(s):  
DAMIR FILIPOVIĆ ◽  
MICHAEL KUPPER
Keyword(s):  
Utility Functions ◽  
Point Of View ◽  
Pricing Rules ◽  
Maximum Utility ◽  
Theoretic Point ◽  
Sufficient And Necessary Conditions ◽  
Game Theoretic ◽  
The Individual ◽  
Monetary Utility Functions ◽  
Consumption Constraints

This paper provides sufficient and necessary conditions for the existence of equilibrium pricing rules for monetary utility functions under convex consumption constraints. These utility functions are characterized by the assumption of a fully fungible numeraire asset ("cash"). Each agent's utility is nominally shifted by exactly the amount of cash added to his endowment. We find the individual maximum utility that each agent is eligible for in an equilibrium and provide a game theoretic point of view for the fair allocation of the aggregate utility.

scholarly journals OPTIMAL RISK SHARING FOR LAW INVARIANT MONETARY UTILITY FUNCTIONS

2008 ◽  
Vol 18 (2) ◽  
pp. 269-292 ◽  
Author(s):  
E. Jouini ◽  
W. Schachermayer ◽  
N. Touzi
Keyword(s):  
Risk Sharing ◽  
Utility Functions ◽  
Monetary Utility Functions ◽  
Optimal Risk Sharing

scholarly journals GENERAL PROPERTIES OF BAYESIAN LEARNING AS STATISTICAL INFERENCE DETERMINED BY CONDITIONAL EXPECTATIONS

2017 ◽  
Vol 10 (4) ◽  
pp. 719-755 ◽  
Author(s):  
ZALÁN GYENIS ◽  
MIKLÓS RÉDEI
Keyword(s):  
Probability Measure ◽  
Probability Space ◽  
Bayesian Learning ◽  
Random Variables ◽  
General Properties ◽  
Extended Space ◽  
Jeffrey Conditionalization ◽  
Conditional Expectations ◽  
Special Cases ◽  
Probability Spaces

AbstractWe investigate the general properties of general Bayesian learning, where “general Bayesian learning” means inferring a state from another that is regarded as evidence, and where the inference is conditionalizing the evidence using the conditional expectation determined by a reference probability measure representing the background subjective degrees of belief of a Bayesian Agent performing the inference. States are linear functionals that encode probability measures by assigning expectation values to random variables via integrating them with respect to the probability measure. If a state can be learned from another this way, then it is said to be Bayes accessible from the evidence. It is shown that the Bayes accessibility relation is reflexive, antisymmetric, and nontransitive. If every state is Bayes accessible from some other defined on the same set of random variables, then the set of states is called weakly Bayes connected. It is shown that the set of states is not weakly Bayes connected if the probability space is standard. The set of states is called weakly Bayes connectable if, given any state, the probability space can be extended in such a way that the given state becomes Bayes accessible from some other state in the extended space. It is shown that probability spaces are weakly Bayes connectable. Since conditioning using the theory of conditional expectations includes both Bayes’ rule and Jeffrey conditionalization as special cases, the results presented generalize substantially some results obtained earlier for Jeffrey conditionalization.

scholarly journals ON ROBUST MULTI-PERIOD PRE-COMMITMENT AND TIME-CONSISTENT MEAN-VARIANCE PORTFOLIO OPTIMIZATION

2017 ◽  
Vol 20 (07) ◽  
pp. 1750049 ◽  
Author(s):  
F. CONG ◽  
C. W. OOSTERLEE
Keyword(s):  
Asset Allocation ◽  
Asset Price ◽  
Time Consistency ◽  
Case Scenario ◽  
Time Step ◽  
Worst Case ◽  
Asset Development ◽  
Robust Portfolio ◽  
Mean Variance Portfolio ◽  
Mean Variance

We consider robust pre-commitment and time-consistent mean-variance optimal asset allocation strategies, that are required to perform well also in a worst-case scenario regarding the development of the asset price. We show that worst-case scenarios for both strategies can be found by solving a specific equation each time step. In the unconstrained asset allocation case, the robust pre-commitment as well as the time-consistent strategy are identical to the corresponding robust myopic strategies, by which investors perform robust portfolio control only for one time step and conduct a risk-free strategy afterwards. In the experiments, the robustness of pre-commitment and time-consistent strategies is studied in detail. Our analysis and numerical results indicate that the time-consistent allocation strategy is more stable when possible incorrect assumptions regarding the future asset development are modeled and taken into account. In some situations, the time-consistent strategy can even generate higher efficient frontiers than the pre-commitment strategy (which is counter-intuitive), because the time-consistency restriction appears to protect an investor in such a situation.

scholarly journals Conditions for the Existence of Absolutely Optimal Portfolios

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2032
Author(s):  
Marius Rădulescu ◽  
Constanta Zoie Rădulescu ◽  
Gheorghiță Zbăganu
Keyword(s):  
Random Vector ◽  
Sufficient Conditions ◽  
Classical Case ◽  
Complete Characterization ◽  
Utility Functions ◽  
Optimal Portfolio ◽  
Optimal Portfolios ◽  
Conditional Expectations ◽  
Necessary And Sufficient ◽  
Bounded Below

Let Δn be the n-dimensional simplex, ξ = (ξ1, ξ2,…, ξn) be an n-dimensional random vector, and U be a set of utility functions. A vector x*∈ Δn is a U -absolutely optimal portfolio if EuξTx*≥EuξTx for every x ∈ Δn and u∈ U. In this paper, we investigate the following problem: For what random vectors, ξ, do U-absolutely optimal portfolios exist? If U2 is the set of concave utility functions, we find necessary and sufficient conditions on the distribution of the random vector, ξ, in order that it admits a U2-absolutely optimal portfolio. The main result is the following: If x0 is a portfolio having all its entries positive, then x0 is an absolutely optimal portfolio if and only if all the conditional expectations of ξi, given the return of portfolio x0, are the same. We prove that if ξ is bounded below then CARA-absolutely optimal portfolios are also U2-absolutely optimal portfolios. The classical case when the random vector ξ is normal is analyzed. We make a complete investigation of the simplest case of a bi-dimensional random vector ξ = (ξ1, ξ2). We give a complete characterization and we build two dimensional distributions that are absolutely continuous and admit U2-absolutely optimal portfolios.

Toward a neuroscope: An application of high-performance computing for real-time evaluation of brain function using MRI

1994 ◽  
Vol 52 ◽  
pp. 922-923
Author(s):  
C. S. Potter ◽  
C. D. Gregory ◽  
H. D. Morris ◽  
Z.-P. Liang ◽  
P. C. Lauterbur
Keyword(s):  
Human Brain ◽  
Brain Function ◽  
High Performance ◽  
Complex Signal ◽  
Time Step ◽  
Brain Organization ◽  
Cognitive Studies ◽  
Positron Emission ◽  
Imaging And Spectroscopy ◽  
3D Anatomy

Over the past few years, several laboratories have demonstrated that changes in local neuronal activity associated with human brain function can be detected by magnetic resonance imaging and spectroscopy. Using these methods, the effects of sensory and motor stimulation have been observed and cognitive studies have begun. These new methods promise to make possible even more rapid and extensive studies of brain organization and responses than those now in use, such as positron emission tomography.Human brain studies are enormously complex. Signal changes on the order of a few percent must be detected against the background of the complex 3D anatomy of the human brain. Today, most functional MR experiments are performed using several 2D slice images acquired at each time step or stimulation condition of the experimental protocol. It is generally believed that true 3D experiments must be performed for many cognitive experiments. To provide adequate resolution, this requires that data must be acquired faster and/or more efficiently to support 3D functional analysis.

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