scholarly journals Time-Consistency of an Imputation in a Cooperative Hybrid Differential Game

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1830
Author(s):  
Ekaterina Gromova ◽  
Anastasiia Zaremba ◽  
Shimai Su
Keyword(s):  
Differential Game ◽  
Cumulative Distribution Function ◽  
Time Consistency ◽  
Analytical Form ◽  
Payoff Function ◽  
Time Inconsistency ◽  
Cumulative Distribution ◽  
Cooperative Solution ◽  
Problem Of Time ◽  
Imputation Distribution Procedure

This work is aimed at studying the problem of maintaining the sustainability of a cooperative solution in an n-person hybrid differential game. Specifically, we consider a differential game whose payoff function is discounted with a discounting function that changes its structure with time. We solve the problem of time-inconsistency of the cooperative solution using a so-called imputation distribution procedure, which was adjusted for this general class of differential games. The obtained results are illustrated with a specific example of a differential game with random duration and a hybrid cumulative distribution function (CDF). We completely solved the presented example to demonstrate the application of the developed scheme in detail. All results were obtained in analytical form and illustrated by numerical simulations.

scholarly journals A Differential Game with Random Time Horizon and Discontinuous Distribution

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2185
Author(s):  
Anastasiia Zaremba ◽  
Ekaterina Gromova ◽  
Anna Tur
Keyword(s):  
Differential Game ◽  
Cumulative Distribution Function ◽  
Finite Interval ◽  
Optimal Solution ◽  
Random Variable ◽  
Cumulative Distribution ◽  
Time Intervals ◽  
The Public ◽  
Random Time Horizon ◽  
Stock Of Knowledge

One class of differential games with random duration is considered. It is assumed that the duration of the game is a random variable with values from a given finite interval. The cumulative distribution function (CDF) of this random variable is assumed to be discontinuous with two jumps on the interval. It follows that the player’s payoff takes the form of the sum of integrals with different but adjoint time intervals. In addition, the first interval corresponds to the zero probability of the game to be finished, which results in terminal payoff on this interval. The method of construction optimal solution for the cooperative scenario of such games is proposed. The results are illustrated by the example of differential game of investment in the public stock of knowledge.

A Method to Quantify Risks of Financial Assets: An Empirical Analysis of Japanese Security Prices

2012 ◽  
Vol 452-453 ◽  
pp. 469-473 ◽  
Author(s):  
Aki Hiro Sato
Keyword(s):  
Distribution Function ◽  
Value At Risk ◽  
Cumulative Distribution Function ◽  
Stock Exchange ◽  
Characteristic Exponent ◽  
Likelihood Estimation ◽  
Estimation Procedure ◽  
Analytical Form ◽  
Cumulative Distribution ◽  
Security Prices

This study investigates unconditional distributions of daily log-returns of Japanese security prices from a comprehensive point of view. The purpose of this article is to estimate a risk distribution of stocks in terms of Value-at-Risk (VaR) in order to select low risk securities from many securities. Daily log-return time series of 1,340 Japanese companies listed on the first section of Tokyo Stock Exchange are examined during the last one decade. I develop a method to estimate VaR by both the maximum likelihood estimation procedure under a q-Gaussian assumption and analytical form of its cumulative distribution function. It is confirmed that they are fitted to q-Gaussian distributions (Student t-distributions) with Kolmogorov-Smirnov test. It is found that the complementary cumulative distribution function of VaR has a power-law tail with its characteristic exponent depending on values of the VaR percentile.

DISSONANCE — A MEASURE OF VARIABILITY FOR ORDINAL RANDOM VARIABLES

2001 ◽  
Vol 09 (01) ◽  
pp. 39-53 ◽  
Author(s):  
RONALD R. YAGER
Keyword(s):  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Probability Distributions ◽  
Random Variables ◽  
Cumulative Distribution ◽  
General Properties

We look at the issue of obtaining a variance like measure associated with probability distributions over ordinal sets. We call these dissonance measures. We specify some general properties desired in these dissonance measures. The centrality of the cumulative distribution function in formulating the concept of dissonance is pointed out. We introduce some specific examples of measures of dissonance.

Estimating the cumulative distribution function for the linear combination of gamma random variables

2017 ◽  
Vol 20 (5) ◽  
pp. 939-951
Author(s):  
Amal Almarwani ◽  
Bashair Aljohani ◽  
Rasha Almutairi ◽  
Nada Albalawi ◽  
Alya O. Al Mutairi
Keyword(s):  
Distribution Function ◽  
Linear Combination ◽  
Cumulative Distribution Function ◽  
Random Variables ◽  
Cumulative Distribution
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