scholarly journals Bias in the estimation of non-linear transformations of the integrated variance of returns

2006 ◽  
Vol 25 (7) ◽  
pp. 481-494 ◽  
Author(s):  
Richard D. F. Harris ◽  
Cherif Guermat
Keyword(s):  
Linear Transformations ◽  
Non Linear ◽  
Integrated Variance

scholarly journals Transformations of Telegraph Processes and Their Financial Applications

Risks ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 147
Author(s):  
Anatoliy A. Pogorui ◽  
Anatoliy Swishchuk ◽  
Ramón M. Rodríguez-Dagnino
Keyword(s):  
Differential Equation ◽  
Stock Prices ◽  
Option Prices ◽  
Linear Transformations ◽  
Financial Applications ◽  
Telegraph Process ◽  
Put Option ◽  
New Models ◽  
Non Linear ◽  
New Applications

In this paper, we consider non-linear transformations of classical telegraph process. The main results consist of deriving a general partial differential Equation (PDE) for the probability density (pdf) of the transformed telegraph process, and then presenting the limiting PDE under Kac’s conditions, which may be interpreted as the equation for a diffusion process on a circle. This general case includes, for example, classical cases, such as limiting diffusion and geometric Brownian motion under some specifications of non-linear transformations (i.e., linear, exponential, etc.). We also give three applications of non-linear transformed telegraph process in finance: (1) application of classical telegraph process in the case of balance, (2) application of classical telegraph process in the case of dis-balance, and (3) application of asymmetric telegraph process. For these three cases, we present European call and put option prices. The novelty of the paper consists of new results for non-linear transformed classical telegraph process, new models for stock prices based on transformed telegraph process, and new applications of these models to option pricing.

Evaluation of Non-Linear and Linear Mathematical Models for Creatinine and Glucose Fitting in Peritoneal Dialysis

1996 ◽  
Vol 19 (4) ◽  
pp. 221-231
Author(s):  
G. Amici
Keyword(s):  
Peritoneal Dialysis ◽  
Concentration Ratio ◽  
Linear Models ◽  
Linear Transformations ◽  
Peritoneal Equilibration Test ◽  
Peritoneal Transport ◽  
Non Linear ◽  
Definition Of ◽  
The Individual ◽  
Fitting In

Four non-linear and five linear models for predicting the creatinine dialysate/plasma ratio (CRD/P) and the glucose dialysate/initial concentration ratio (GLD/Do) were evaluated in a group of 31 patients on peritoneal dialysis and subjected to the peritoneal equilibration test (PET 3.86%, 240'). PET results and classification were compared to obtain a definition of patient peritoneal transport characteristics. The monomolecular and rectangular hyperbola non-linear models, the Lineweaver-Burk, Hanes-Woolf and Dadone linear transformations were considered for the CRD/P fitting. A monoexponential and two-exponential decay plus the semilogarithmic transformations were considered for the GLD/Do. These models are simple, accurate and functionally homogeneous. Further studies are advisable however on the individual peritoneal transport classification, since ∼30% of the patients were in different categories for CRD/P and GLD/Do and the fittings do not give better classification results.

Some Transformations of Hausdorff Moment Sequences and Harmonic Numbers

2005 ◽  
Vol 57 (5) ◽  
pp. 941-960 ◽  
Author(s):  
Christian Berg ◽  
Antonio J. Durán
Keyword(s):  
Harmonic Numbers ◽  
Linear Transformations ◽  
Non Linear ◽  
The One

AbstractWe introduce some non-linear transformations from the set of Hausdorff moment sequences into itself; among them is the one defined by the formula: . We give some examples of Hausdorff moment sequences arising from the transformations and provide the corresponding measures: one of these sequences is the reciprocal of the harmonic numbers .

DYNAMICAL SYSTEMS FROM QUANTUM INTEGRABILITY

1993 ◽  
Vol 07 (20n21) ◽  
pp. 3567-3596 ◽  
Author(s):  
M.P. Bellon ◽  
J-M. Maillard ◽  
C-M. Viallet
Keyword(s):  
Dynamical Systems ◽  
Projective Spaces ◽  
Linear Transformations ◽  
Quantum Integrability ◽  
Higher Dimensional ◽  
Algebraic Invariants ◽  
Non Linear ◽  
Birational Mappings

We describe a class of non-linear transformations acting on many variables. These transformations have their origin in the theory of quantum integrability: they appear in the description of the symmetries of the Yang-Baxter equations and their higher dimensional generalizations. They are generated by involutions and act as birational mappings on various projective spaces. We present numerous figures, showing successive iterations of these mappings. The existence of algebraic invariants explains the aspect of these figures. We also study deformations of our transformations.

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