New general solutions to the Abel equation of the second kind using functional transformations

Salinas-Hernández, E.; Martínez-Castro, J.; Munoz, R Raul Pagan

doi:10.1016/j.amc.2012.02.003

Cited by 7 publications

(5 citation statements)

References 10 publications

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“…Let's take the canonic equation (14) z = z 3 + Φ. Now, try the following simple trick: add and substract the term ϕz in which ϕ is a free function, that is…”

Section: First Proposal Of Solutionmentioning

confidence: 99%

“…Let us now consider some cases which are obtained from the solution found from (14), which are obviously analytic. These are shown below.…”

Section: Second Proposal For Solutionmentioning

confidence: 99%

“…al. get analitycal solutions for Abel's differential equation of second kind using functional transformations [14]. The references [15,3] use computational algorithms to solve such equation.…”

Section: Introductionmentioning

confidence: 99%

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Analysis to the solutions of Abel's differential equation of the first kind under the transformation y=u(x)z(x)+v(x)

Salinas-Hernández¹,

Muñoz-Vega²,

Sosa³

et al. 2013

ams

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In this work we study different analytical solutions which can be obtained from a new Abel equation of first kind, under the transformation 2076 E. Salinas-Hernández et al. y = u(x)z(x) + v(x), changing the variable to z(x), where the coefficients of this equation allow the construction of a system of auxiliary equation with φ 1 (x), φ 2 (x) and φ 3 (x) as free functions to the system. From the form of the system, different cases are obtained, whose details are described in this work.

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“…Let's take the canonic equation (14) z = z 3 + Φ. Now, try the following simple trick: add and substract the term ϕz in which ϕ is a free function, that is…”

Section: First Proposal Of Solutionmentioning

confidence: 99%

“…Let us now consider some cases which are obtained from the solution found from (14), which are obviously analytic. These are shown below.…”

Section: Second Proposal For Solutionmentioning

confidence: 99%

See 1 more Smart Citation

Analysis to the solutions of Abel's differential equation of the first kind under the transformation y=u(x)z(x)+v(x)

Salinas-Hernández¹,

Muñoz-Vega²,

Sosa³

et al. 2013

ams

View full text Add to dashboard Cite

show abstract

“…The application of Abel Equation in finance is rare [3][4][5][6][7][8][9][10] . In this paper, we try to apply Abel Equation for the option pricing in financial derivatives with several ETFs in the market.…”

Section: Introductionmentioning

confidence: 99%

Option Pricing Approach and Its Application Based on Abel Equation

Ying¹,

Guo²

2020

Proceedings of the International Conference on Arts, Humanity and Economics, Management (ICAHEM 2019)

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Financial derivative is one kind of financial instrument with high leverage ratio, high risk and high returns. Therefore, in it important to help investors to adopt appropriate risk control measures to judge the trend of the price change of financial derivatives. The trend of financial derivatives prices has been analyzed by solving the responding Abel equation. At last, we illustrate the scheme by testing several ETFs in the market for the system.

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“…The case r D 0 has been introduced more than 200 years ago by Abel [1]. Many solvable equations of this type are collected in [2], and other ones can be found in more recent works [3][4][5][6][7][8][9]. The transformation 1=y D w C s converts this equation in the form dy dx D r C .q 2 3rs/y C Â q 1 ds dx 2q 2 s C 3rs 2 Ã y 2 C .p q 1 s C q 2 s 2 rs 3 /y 3 ,…”

Section: Introductionmentioning

confidence: 99%