scholarly journals ON FINITE DIMENSIONAL REALIZATIONS FOR THE TERM STRUCTURE OF FUTURES PRICES

2006 ◽  
Vol 09 (03) ◽  
pp. 281-314 ◽  
Author(s):  
TOMAS BJÖRK ◽  
MAGNUS BLIX ◽  
CAMILLA LANDÉN
Keyword(s):  
Term Structure ◽  
State Space Model ◽  
Sufficient Conditions ◽  
Algebraic Approach ◽  
Necessary And Sufficient Conditions ◽  
Spot Price ◽  
Futures Prices ◽  
Finite Dimensional ◽  
Futures Price ◽  
Necessary And Sufficient

We consider HJM type models for the term structure of futures prices, where the volatility is allowed to be an arbitrary smooth functional of the present futures price curve. Using a Lie algebraic approach we investigate when the infinite dimensional futures price process can be realized by a finite dimensional Markovian state space model, and we give general necessary and sufficient conditions, in terms of the volatility structure, for the existence of a finite dimensional realization. We study a number of concrete applications including a recently developed model for gas futures. In particular we provide necessary and sufficient conditions for when the induced spot price is a Markov process. In particular we can prove that the only HJM type futures price models with spot price dependent volatility structures which generically possess a spot price realization are the affine ones. These models are thus the only generic spot price models from a futures price term structure point of view.

CONSISTENT PARALLEL AND PROPORTIONAL SHIFTS IN THE TERM STRUCTURE OF FUTURES PRICES

2015 ◽  
Vol 18 (01) ◽  
pp. 1550006
Author(s):  
MIA HINNERICH
Keyword(s):  
Term Structure ◽  
Marked Point ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Marked Point Process ◽  
Single Factor ◽  
Price Model ◽  
Futures Price ◽  
Necessary And Sufficient ◽  
Multidimensional Wiener Process

We consider an arbitrage-free futures price model of Heath–Jarrow–Morton type which is driven by a multidimensional Wiener process and a marked point process. We find necessary and sufficient conditions for this model to produce a log futures curve that changes only through parallel shifts. The same analysis is carried out for the case when the log futures curve changes only through proportional shifts. We prove that there exist nontrivial parallel and proportional shifting log futures curves and we show how to specify the futures price model in order to obtain them. Additionally the shift functions are characterized. Finally, we consider the case of all other single-factor affine models which are neither parallel nor proportional shifting curves. We find necessary and sufficient conditions for the purely Wiener-driven log futures model to admit such other affine shifting curve and we characterize the shift functions.

scholarly journals Graded modules over simple Lie algebras

2019 ◽  
Vol 53 (supl) ◽  
pp. 45-86
Author(s):  
Yuri Bahturin ◽  
Mikhail Kochetov ◽  
Abdallah Shihadeh
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Arbitrary Dimension ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Simple Lie Algebras ◽  
Simple Modules ◽  
Graded Modules ◽  
Finite Dimensional ◽  
Necessary And Sufficient

The paper is devoted to the study of graded-simple modules and gradings on simple modules over finite-dimensional simple Lie algebras. In general, a connection between these two objects is given by the so-called loop construction. We review the main features of this construction as well as necessary and sufficient conditions under which finite-dimensional simple modules can be graded. Over the Lie algebra sl2(C), we consider specific gradings on simple modules of arbitrary dimension.

Titling pair over split-by-nilpotent extensions

2020 ◽  
pp. 2250019
Author(s):  
Dajun Liu ◽  
Jiaqun Wei
Keyword(s):  
Similar Condition ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Split Extension ◽  
Finite Dimensional ◽  
Necessary And Sufficient ◽  
Finite Dimensional Algebras

Let [Formula: see text], [Formula: see text] be two finite dimensional algebras over a field [Formula: see text], such that [Formula: see text] is a split extension of A by the nilpotent bimodule [Formula: see text]. We mainly give necessary and sufficient conditions for a tilting pair [Formula: see text] such that [Formula: see text] or [Formula: see text] are tilting pairs. Also, we obtain a similar condition such that a Wakamatsu tilting pair [Formula: see text] in [Formula: see text]-mod can be a Wakamatsu tilting pair [Formula: see text] in [Formula: see text]-mod.

scholarly journals POINTED HOPF ALGEBRAS WITH CLASSICAL WEYL GROUPS

2012 ◽  
Vol 23 (06) ◽  
pp. 1250066
Author(s):  
SHOUCHUAN ZHANG ◽  
YAO-ZHONG ZHANG
Keyword(s):  
Hopf Algebras ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Weyl Groups ◽  
Drinfeld Modules ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Pointed Hopf Algebras ◽  
Nichols Algebras ◽  
Necessary And Sufficient

We prove that Nichols algebras of irreducible Yetter–Drinfeld modules over classical Weyl groups A ⋊ 𝕊nsupported by 𝕊nare infinite dimensional, except in three cases. We give necessary and sufficient conditions for Nichols algebras of Yetter–Drinfeld modules over classical Weyl groups A ⋊ 𝕊nsupported by A to be finite dimensional.

Kan Extensions of Internal Functors. Algebraic Approach

1999 ◽  
Vol 6 (2) ◽  
pp. 127-148
Author(s):  
T. Datuashvili
Keyword(s):  
Sufficient Conditions ◽  
Algebraic Approach ◽  
Necessary And Sufficient Conditions ◽  
Kan Extensions ◽  
Necessary And Sufficient ◽  
Categories And Functors

Abstract We investigate the question of the Kan extension in the case when all categories and functors are internal in the category of groups. Under certain assumptions we establish the necessary and sufficient conditions for the existence of internal Kan extensions. Questions related to this problem are also discussed.

scholarly journals Necessary and Sufficient Conditions for Complementary Stochastic Quadratic Operators of Finite-Dimensional Simplex

2017 ◽  
Vol 1 (1) ◽  
pp. 22 ◽  
Author(s):  
Rawad Abdulghafor ◽  
Sherzod Turaev ◽  
Akram Zeki
Keyword(s):  
Dimensional Space ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Finite Dimensional Space ◽  
Quadratic Operator ◽  
Dimensional Simplex ◽  
Quadratic Stochastic Operator ◽  
Finite Dimensional ◽  
Stochastic Operator ◽  
Necessary And Sufficient

We define a complementary stochastic quadratic operator on finite-dimensional space as a new sub-class of quadratic stochastic operator. We give necessary and sufficient conditions for complementary stochastic quadratic operator.  

Sets of Generators of a Commutative and Associative Algebra(1)

1971 ◽  
Vol 14 (3) ◽  
pp. 315-319
Author(s):  
D. Ž. Djoković
Keyword(s):  
Recent Result ◽  
Associative Algebra ◽  
Polynomial Algebra ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Quotient Algebra ◽  
Algebra 1 ◽  
Finite Dimensional ◽  
Necessary And Sufficient ◽  
Special Case

AbstractLet A be a finite dimensional commutative and associative algebra with identity, over a field K. We assume also that A is generated by one element and consequently, isomorphic to a quotient algebra of the polynomial algebra K[X]. If A=K[a] and bi=fi(A), fi(X) ∊ K[X], 1≤i≤r we find necessary and sufficient conditions which should be satisfied by fi(X) in order that A = K[b1, …, br].The result can be stated as a theorem about matrices. As a special case we obtain a recent result of Thompson [4].In fact this last result was established earlier by Mirsky and Rado [3]. I am grateful to the referee for supplying this reference.

scholarly journals SKIPPED BLOCKING AND OTHER DECOMPOSITIONS IN BANACH SPACES

2006 ◽  
Vol 17 (02) ◽  
pp. 129-141
Author(s):  
STEVEN F. BELLENOT
Keyword(s):  
Banach Spaces ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Separable Space ◽  
Finite Dimensional ◽  
Necessary And Sufficient

Necessary and sufficient conditions are given for when a sequence of finite-dimensional subspaces (Xn) can be blocked to be a skipped blocking decompositon (SBD). These are very similar to known results about blocking of biorthogonal sequences. A separable space X has PCP, if and only if, every norming decomposition (Xn) can be blocked to be a boundedly complete SBD. Every boundedly complete SBD is a JT-decomposition.

COPULA-BASED CHARACTERIZATIONS FOR HIGHER ORDER MARKOV PROCESSES

2009 ◽  
Vol 25 (3) ◽  
pp. 819-846 ◽  
Author(s):  
Rustam Ibragimov
Keyword(s):  
Time Series ◽  
Markov Processes ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Necessary And Sufficient Conditions ◽  
Conditional Symmetry ◽  
Finite Dimensional ◽  
Necessary And Sufficient ◽  
Dependence Properties

In this paper, we obtain characterizations of higher order Markov processes in terms of copulas corresponding to their finite-dimensional distributions. The results are applied to establish necessary and sufficient conditions for Markov processes of a given order to exhibitm-dependence,r-independence, or conditional symmetry. The paper also presents a study of applicability and limitations of different copula families in constructing higher order Markov processes with the preceding dependence properties. We further introduce new classes of copulas that allow one to combine Markovness withm-dependence orr-independence in time series.

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