Integration with respect to fractal functions and stochastic calculus. I

1998 ◽  
Vol 111 (3) ◽  
pp. 333-374 ◽  
Author(s):  
M. Zähle
Keyword(s):  
Stochastic Calculus ◽  
Calculus I ◽  
Fractal Functions

scholarly journals The Black-Scholes Model Guideline For Options Course As Taught At Notre Dame University - Lebanon

2011 ◽  
Vol 4 (1) ◽  
Author(s):  
Viviane Y. Naimy
Keyword(s):  
Option Price ◽  
Stochastic Calculus ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Calculus I ◽  
Relationship Of ◽  
The Relationship

This paper presents the methodology used for Notre Dame University’s finance students to explain and explore the Black-Scholes model without going through the complexity of mathematics to model random movements or through stochastic calculus. I will name and develop the steps that I follow in order to allow students to properly use the Black-Scholes model and to understand the relationship of the model’s inputs to the option price while monitoring the risk via delta and gamma hedging.

scholarly journals Semilinear fractional stochastic differential equations driven by a γ-Hölder continuous signal with γ > 2/3

2020 ◽  
Vol 21 (01) ◽  
pp. 2050039
Author(s):  
Jorge A. León ◽  
David Márquez-Carreras
Keyword(s):  
Acta Math ◽  
Stochastic Calculus ◽  
Initial Condition ◽  
Hölder Continuous ◽  
Fractional Stochastic Differential Equations ◽  
Stieltjes Integration ◽  
Fractal Functions ◽  
Fractional Differential ◽  
Young Integral ◽  
Semilinear Fractional Differential Equation

In this paper, we use the techniques of fractional calculus to study the existence of a unique solution to semilinear fractional differential equation driven by a [Formula: see text]-Hölder continuous function [Formula: see text] with [Formula: see text]. Here, the initial condition is a function that may not be defined at zero and the involved integral with respect to [Formula: see text] is the extension of the Young integral [An inequality of the Hölder type, connected with Stieltjes integration, Acta Math. 67 (1936) 251–282] given by Zähle [Integration with respect to fractal functions and stochastic calculus I, Probab. Theory Related Fields 111 (1998) 333–374].

STUDENT INTERACTIONS WITH PREREQUISITE KNOWLEDGE TOOLS: HOW STUDENTS' DAILY-USAGE PATTERNS CAN INFORM PEDAGOGY IN CALCULUS I

2019 ◽  
Vol 16 (2) ◽  
pp. 14
Author(s):  
FOLKESTAD JAMES ◽  
E. PILGRIM MARY ◽  
SENCINDIVER BEN ◽  
HARINDRANATHAN PRIYA ◽  
◽  
...  
Keyword(s):  
Student Interactions ◽  
Calculus I ◽  
Usage Patterns ◽  
Prerequisite Knowledge
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