# Analytical Solutions of the Black–Scholes Pricing Model for European Option Valuation via a Projected Differential Transformation Method

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## Abstract

**:**

## 1. Introduction

## 2. The Differential Transformation Method (DTM) and Its Modification

#### 2.1. Analysis of a Two-Dimensional DTM

**Theorem 2.**

**Theorem 3.**

**Theorem 4.**

**Theorem 5.**

#### 2.2. The Overview of the PDTM

#### 2.3. Some Fundamental Theorems and Properties of the PDTM

**Theorem 6.**

**Theorem 7a.**

**Theorem 7b.**

**Theorem 8.**

**Theorem 9.**

## 3. Applications and Illustrative Examples

**Example 1.**

## 4. Discussion of Results

## 5. Concluding Remarks

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**MDPI and ACS Style**

Edeki, S.O.; Ugbebor, O.O.; Owoloko, E.A.
Analytical Solutions of the Black–Scholes Pricing Model for European Option Valuation via a Projected Differential Transformation Method. *Entropy* **2015**, *17*, 7510-7521.
https://doi.org/10.3390/e17117510

**AMA Style**

Edeki SO, Ugbebor OO, Owoloko EA.
Analytical Solutions of the Black–Scholes Pricing Model for European Option Valuation via a Projected Differential Transformation Method. *Entropy*. 2015; 17(11):7510-7521.
https://doi.org/10.3390/e17117510

**Chicago/Turabian Style**

Edeki, Sunday O., Olabisi O. Ugbebor, and Enahoro A. Owoloko.
2015. "Analytical Solutions of the Black–Scholes Pricing Model for European Option Valuation via a Projected Differential Transformation Method" *Entropy* 17, no. 11: 7510-7521.
https://doi.org/10.3390/e17117510