scholarly journals Extended conditional G-expectations and related stopping times

2021 ◽  
Vol 6 (4) ◽  
pp. 369
Author(s):  
Mingshang Hu ◽  
Shige Peng
Keyword(s):  
Random Variable ◽  
Careful Analysis ◽  
Stopping Times ◽  
Monotone Sequence ◽  
Optional Stopping ◽  
Suitable Definition ◽  
Dynamical Consistency ◽  
Definition Of

<p style='text-indent:20px;'>In this paper, we extend the definition of conditional <inline-formula> <tex-math id="M2">\begin{document}$ G{\text{-}}{\rm{expectation}} $\end{document}</tex-math> </inline-formula> to a larger space on which the dynamical consistency still holds. We can consistently define, by taking the limit, the conditional <inline-formula> <tex-math id="M3">\begin{document}$ G{\text{-}}{\rm{expectation}} $\end{document}</tex-math> </inline-formula> for each random variable <inline-formula> <tex-math id="M4">\begin{document}$ X $\end{document}</tex-math> </inline-formula>, which is the downward limit (respectively, upward limit) of a monotone sequence <inline-formula> <tex-math id="M5">\begin{document}$ \{X_{i}\} $\end{document}</tex-math> </inline-formula> in <inline-formula> <tex-math id="M6">\begin{document}$ L_{G}^{1}(\Omega) $\end{document}</tex-math> </inline-formula>. To accomplish this procedure, some careful analysis is needed. Moreover, we present a suitable definition of stopping times and obtain the optional stopping theorem. We also provide some basic and interesting properties for the extended conditional <inline-formula> <tex-math id="M7">\begin{document}$ G{\text{-}}{\rm{expectation}} $\end{document}</tex-math> </inline-formula>. </p>

scholarly journals Real-Option Valuation in Multiple Dimensions Using Poisson Optional Stopping Times

2019 ◽  
Vol 55 (2) ◽  
pp. 653-677 ◽  
Author(s):  
Rutger-Jan Lange ◽  
Daniel Ralph ◽  
Kristian Støre
Keyword(s):  
Real Option ◽  
Value Function ◽  
Stopping Times ◽  
Monotone Sequence ◽  
Option Valuation ◽  
Real Option Valuation ◽  
Multiple Dimensions ◽  
Optional Stopping ◽  
New Framework

We provide a new framework for valuing multidimensional real options where opportunities to exercise the option are generated by an exogenous Poisson process, which can be viewed as a liquidity constraint on decision times. This approach, which we call the Poisson optional stopping times (POST) method, finds the value function as a monotone sequence of lower bounds. In a case study, we demonstrate that the frequently used quasi-analytic method yields a suboptimal policy and an inaccurate value function. The proposed method is demonstrably correct, straightforward to implement, reliable in computation, and broadly applicable in analyzing multidimensional option-valuation problems.

An LQ Approach to Active Control of Vibrations in Helicopters

1996 ◽  
Vol 118 (3) ◽  
pp. 482-488 ◽  
Author(s):  
Sergio Bittanti ◽  
Fabrizio Lorito ◽  
Silvia Strada
Keyword(s):  
Optimal Control ◽  
Active Control ◽  
Linear Quadratic ◽  
Control Effort ◽  
Vibration Effect ◽  
Suitable Definition ◽  
Lq Optimal Control ◽  
The One ◽  
Definition Of ◽  
And Control

In this paper, Linear Quadratic (LQ) optimal control concepts are applied for the active control of vibrations in helicopters. The study is based on an identified dynamic model of the rotor. The vibration effect is captured by suitably augmenting the state vector of the rotor model. Then, Kalman filtering concepts can be used to obtain a real-time estimate of the vibration, which is then fed back to form a suitable compensation signal. This design rationale is derived here starting from a rigorous problem position in an optimal control context. Among other things, this calls for a suitable definition of the performance index, of nonstandard type. The application of these ideas to a test helicopter, by means of computer simulations, shows good performances both in terms of disturbance rejection effectiveness and control effort limitation. The performance of the obtained controller is compared with the one achievable by the so called Higher Harmonic Control (HHC) approach, well known within the helicopter community.

scholarly journals Fractional negative binomial and Pólya processes

2018 ◽  
Vol 38 (1) ◽  
pp. 77-101
Author(s):  
Palaniappan Vellai Samy ◽  
Aditya Maheshwari
Keyword(s):  
Poisson Process ◽  
Negative Binomial ◽  
Random Variable ◽  
Infinitely Divisible ◽  
One Dimensional ◽  
Fractional Poisson Process ◽  
Negative Binomial Process ◽  
The One ◽  
Definition Of ◽  
Binomial Process

In this paper, we define a fractional negative binomial process FNBP by replacing the Poisson process by a fractional Poisson process FPP in the gamma subordinated form of the negative binomial process. It is shown that the one-dimensional distributions of the FPP and the FNBP are not infinitely divisible. Also, the space fractional Pólya process SFPP is defined by replacing the rate parameter λ by a gamma random variable in the definition of the space fractional Poisson process. The properties of the FNBP and the SFPP and the connections to PDEs governing the density of the FNBP and the SFPP are also investigated.

Indigenato Before Race? Some Proposals on Portuguese Forced Labour Law in Mozambique and the African Empire (1926–62)

2012 ◽  
Author(s):  
MICHEL CAHEN
Keyword(s):  
Careful Analysis ◽  
Native People ◽  
Smooth Transition ◽  
Skin Colour ◽  
Labour Law ◽  
Capitalist Economy ◽  
Social Sphere ◽  
Key Factor ◽  
Forced Labour ◽  
Definition Of

Was blackness the key factor for labelling native people as ‘non-civilised’ and thus to be pushed into forced labour in Portuguese Africa? Without denying the importance of blackness as a stigmatising tool, this chapter argues, through a careful analysis of colonial law and practice, that the production of ‘nativeness’ was related to clear consciousness of Africans living outside the capitalist economy and social sphere. This helps us to understand that emerging forced labour represented not a smooth transition from slavery, but a rupture between two colonial ages and modes of production. Therefore, if colonial racism obviously used skin colour to construct a social bar, above all it used the definition of otherness as external to the capitalist sphere. Petty whites and natives could live side by side in suburban neighbourhoods, but in two impermeable spheres. Racism was pervasively present, but it was more social than racial.

scholarly journals On the Inversion of the Gauss Transformation

1957 ◽  
Vol 9 ◽  
pp. 459-464 ◽  
Author(s):  
P. G. Rooney
Keyword(s):  
Differential Operator ◽  
Recent Work ◽  
Suitable Definition ◽  
Inversion Theory ◽  
The Subject ◽  
Definition Of ◽  
Image Position ◽  
Gauss Transformation ◽  
Operational Methods

The inversion theory of the Gauss transformation has been the subject of recent work by several authors. If the transformation is defined by1.1,then operational methods indicate that,under a suitable definition of the differential operator.

A regression problem

1951 ◽  
Vol 47 (2) ◽  
pp. 337-346
Author(s):  
D. V. Lindley
Keyword(s):  
Complete Solution ◽  
Practical Importance ◽  
Random Variable ◽  
Partial Solution ◽  
Point Of View ◽  
General Definition ◽  
Regression Problem ◽  
Definition Of ◽  
Regression Theory ◽  
Complete Solutions

During the Oxford Conference of the Econometric Society in September 1936, Ragnar Frisch proposed a problem in regression theory. A partial solution was found in 1938 by Miss H. V. Allen (1). A more complete solution was given by C. R. Rao (6) in 1947, and in the same year the present author (5) obtained a solution as a particular case of a more general result. These last two papers contained a flaw, and a correct solution was provided by Miss E. Fix (2). This last solution still leaves a part of the problem unanswered, and in the present paper a result of P. Lévy's (4), is used to complete the solution. At the same time further generalizations of the problem are considered and, in the cases of most practical importance, complete solutions are obtained. It is advisable, both from the point of view of rigour and simplicity of analysis, to use a general definition of the conditional expectation of a random variable. Accordingly, the paper begins with a summary of the relevant definitions. These notions were introduced by Kolmogoroff (3). It has been thought worth while giving the definitions here, in forms which are slightly different from Kolmogoroff's and seem more suitable for applications, in order to explain the notation and nomenclature used. The relevant consequences of these definitions are also stated in the form in which they are used.

The Algebra of Dimension-Linking Operators

1965 ◽  
Vol 8 (2) ◽  
pp. 203-222 ◽  
Author(s):  
R. H. Bruck
Keyword(s):  
Group Theory ◽  
Special Reference ◽  
Mathematical Society ◽  
Summer Institute ◽  
Burnside Problem ◽  
The Third ◽  
Australian Mathematical Society ◽  
Suitable Definition ◽  
Definition Of ◽  
Restricted Burnside Problem

In the course of preparing a book on group theory [1] with special reference to the Restricted Burnside Problem and allied problems I stumbled upon the concept of a dimension-linking operator. Later, when I lectured to the Third Summer Institute of the Australian Mathematical Society [2], G. E. Wall raised the question whether the dimension-linking operators could be made into a ring by introduction of a suitable definition of multiplication. The answer was easily found to be affirmative; the result wasthat the theory of dimen sion-linking operators became exceedingly simple.

scholarly journals On Near-Rings of Quotients

1979 ◽  
Vol 22 (2) ◽  
pp. 77-86 ◽  
Author(s):  
A. Oswald
Keyword(s):  
Finite Rank ◽  
Minimum Condition ◽  
Suitable Definition ◽  
Definition Of ◽  
Rings Of Quotients

In (2), Holcombe investigated near-rings of zero-preserving mappings of a group Γ which commute with the elements of a semigroup S of endomorphisms of Γ and examined the question: under what conditions do near-rings of this type have near-rings of right quotients which are 2-primitive with minimum condition on right ideals? In the first part of this paper (§2) we investigate further properties of near-rings of this type. The second part of the paper (§3) deals with those near-rings which have semisimple near-rings of right quotients. Our results here are analogous to those of Goldie (1); in particular, with a suitable definition of finite rank we prove that a near-ring which has a semisimple near-ring of right quotients has finite rank

Republic Book one on the Nature of Justice

2008 ◽  
Vol 25 (1) ◽  
pp. 63-78
Author(s):  
T.F. Morris
Keyword(s):  
Careful Analysis ◽  
Ulterior Motive ◽  
The Future ◽  
True Position ◽  
Definition Of ◽  
Wage Earning

Even though the first book of the Republic ends with the claim that the definition of justice has not been determined, a careful analysis of the details of Socrates’ arguments with Polemarchus and Thrasymachus yields a definition of justice. Polemarchus should have defended the understanding of justice as helping friends and harming enemies by saying that, because one can use one’s knowledge either to help or to harm, a just person will choose to use his knowledge of an art either to help his friends or to harm his enemies. Socrates’ art of wage-earning is not really an art at all, but merely amounts to having an ulterior motive for doing what one does. Socrates’ true position will be seen to be that just people use their knowledge for the sake of helping people—not for the sake of acquiring some supposed benefit for themselves in the future.

GENERALIZED MEASURE OF UNCERTAINTY AND THE MAXIMIZABLE ENTROPY

2010 ◽  
Vol 24 (09) ◽  
pp. 825-831 ◽  
Author(s):  
CONGJIE OU ◽  
AZIZ EL KAABOUCHI ◽  
JINCAN CHEN ◽  
ALAIN LE MÉHAUTÉ ◽  
ALEXANDRE QIUPING WANG
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Statistical Methods ◽  
Physical Meaning ◽  
Probability Distribution Function ◽  
Random Variable ◽  
Uncertainty Measure ◽  
Definition Of ◽  
Measure Of Uncertainty

For a random variable x we can define a variational relationship with practical physical meaning as [Formula: see text], where I is the uncertainty measure. With the help of a generalized definition of expectation, [Formula: see text], we can find the concrete forms of the maximizable entropies for any given probability distribution function, where g({pi}) may have different forms for different statistical methods which include the extensive and non-extensive statistics. Moreover, it is pointed out that this generalized uncertainty measure is valid not only for thermodynamic systems but also for non-thermodynamic systems.

Sign in / Sign up

Export Citation Format

Share Document