scholarly journals New Symmetries of Black-Scholes Equation

2021 ◽  
Vol 20 ◽  
pp. 76-87
Author(s):  
Tshidiso Masebe
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
Linear Differential Equations ◽  
Lie Point Symmetries ◽  
Invariant Solutions ◽  
One Dimensional ◽  
Black Scholes ◽  
Linear Differential ◽  
The One ◽  
Ordinary Linear Differential Equations

Lie Point symmetries and Euler’s formula for solving second order ordinary linear differential equations are used to determine symmetries for the one-dimensional Black- Scholes equation. One symmetry is utilized to determine an invariant solutions

scholarly journals Composition sum identities related to the distribution of coordinate values in a discrete simplex

10.37236/1498 ◽  
2000 ◽  
Vol 7 (1) ◽  
Author(s):  
R. Milson
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
Linear Differential Equations ◽  
Algebraic Methods ◽  
Algebraic Proof ◽  
Geometric Properties ◽  
Linear Differential ◽  
Exponential Formula ◽  
Ordinary Linear Differential Equations ◽  
General Method

Utilizing spectral residues of parameterized, recursively defined sequences, we develop a general method for generating identities of composition sums. Specific results are obtained by focusing on coefficient sequences of solutions of first and second order, ordinary, linear differential equations. Regarding the first class, the corresponding identities amount to a proof of the exponential formula of labelled counting. The identities in the second class can be used to establish certain geometric properties of the simplex of bounded, ordered, integer tuples. We present three theorems that support the conclusion that the inner dimensions of such an order simplex are, in a certain sense, more ample than the outer dimensions. As well, we give an algebraic proof of a bijection between two families of subsets in the order simplex, and inquire as to the possibility of establishing this bijection by combinatorial, rather than by algebraic methods.

scholarly journals A Relation between two Ordinary Linear Differential Equations of the Second Order

1935 ◽  
Vol 29 ◽  
pp. ix-xi
Author(s):  
D. G. Taylor
Keyword(s):  
Differential Equations ◽  
Order Equation ◽  
Second Order ◽  
Linear Differential Equations ◽  
Independent Variable ◽  
Linear Differential ◽  
Image Position ◽  
Ordinary Linear Differential Equations

1. Between the solutions of the equationsa relation can be established, provided the functional symbols f, ø are inverse to one another. For example, let f (x) = sin x, then ø(ξ)= arcsin ξ, and the two equations areThe process consists in obtaining from (1) the second order equation satisfied by yx = dy/dx, making a change of independent variable in (2), and comparing the resulting equations.

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