analysis and linear algebra for finance 1

Patrick Roger
Analysis and Linear Algebra for
Finance: Part I
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2

Patrick Roger
Analysis and Linear Algebra for Finance:
Part I
Patrick ROGER
LaRGE Research Center
EM Strasbourg Business School
University of Strasbourg
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3

Analysis and Linear Algebra for Finance: Part I
First edition
© 2013 Patrick Roger &
bookboon.com (Ventus Publishing ApS)
ISBN 978-87-403-0412-1
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Analysis and Linear Algebra for Finance: Part I
4

Contents
Contents
Introduction 6
1 Preliminaries 7

1.1 Sets and subsets 8
1.2 Binary relations 17
1.3 Mappings 20
1.4 Topology of
    
             
               
 

               
              
  
          
           
         
 
         
           
            
    
              
             
           
   
          
              
      
                
                  
           

        

                
               
25
2 Functions of one variable 43
2.1 Denitions and notations 44
2.2 Limits and continuity 50
2.3 Dierentiation 61
2.4 Logarithms and exponential functions 70
2.5 Polynomial approximations and Taylor formula 75
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Analysis and Linear Algebra for Finance: Part I
5

Contents
3 Integrals 81
3.1 Integral of a step function 81
3.2 General case 86
3.3 Computations 94
3.4 Improper integrals 98
4 Matrices 101
4.1 Denitions 101
4.2 Elementary algebra on matrices 104
4.3 Linear equations 115
360°
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Analysis and Linear Algebra for Finance: Part I
6

Introduction
 

        

    
          

  
          

           
          
          
            
         
          
          
            
           
       
         
          
             
         

           
            
          
         
         
             

          
  
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          
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Analysis and Linear Algebra for Finance: Part I
7

Preliminaries
 

         
          
            
        
          
           
             
          
 
        
          
            
            
     

    
            
             
              
            

          

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Analysis and Linear Algebra for Finance: Part I
8

Preliminaries
   
            
          
            
        
   
            
           
            
              
          
           
       
             
     

    
            
           
            
    
   
             
      
                   


            
   

              
      
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Analysis and Linear Algebra for Finance: Part I
9

Preliminaries
    
                   

            

               
  
                  
                
      
          


 
      
              
       
 

     

 



         

             
             
              
  
             
    
            
  

         
             