Conference PaperPDF Available

-دور الرياضيات في اتخاذ القرار الاستثماري -دراسة تطبيقية لمعياري التوقع الرياضي والتباين

Authors:

Abstract

الاستثمار هو عملية تحديد المستقبل واتخاذ قرارات تأثيرية تحمل مخاطر وفرصًا. تواجه القرارات الاستثمارية المستثمرين بتحدٍ وفرصة لا يمكن تجاهلهما، وهم يسعون دائمًا لاتخاذ القرار الأمثل لتحقيق مكاسب مالية. إن أمام المستثمرين تحدي كبير يتعلق بتحليل البيانات والأرقام وتقدير المخاطر والمكاسب المحتملة. هنا تأتي أهمية الرياضيات بقوتها. الرياضيات ليست مجرد علم نظري بل هي أداة قوية تمكن من تحليل المعلومات وصياغة استنتاجات دقيقة. في عالم الاستثمار، يمكن للرياضيات توجيه القرارات وزيادة دقتها. سواء كنت تحاول تقدير القيمة الحالية لاستثمار محدد أو تحليل الأسهم أو إدارة محفظة استثمارية، فإن الرياضيات تمنحك أدوات قوية لاتخاذ قرارات مستنيرة ان هذا البحث يهدف إلى استكشاف الدور المحوري الذي تلعبه الرياضيات في اتخاذ القرارات الاستثمارية. سنبحث في كيفية استخدام النماذج الرياضية والتحليل الكمي في تقدير القيمة وإدارة المخاطر وتحسين الأداء الاستثماري. سنعرض دراسات حالة وتطبيقات عملية لتوضيح كيفية استخدام الرياضيات لاتخاذ قرارات استثمارية ذكية Investment is a process of forecasting the future and making influential decisions that carry both risks and opportunities. Investment decisions present investors with challenges and opportunities they cannot ignore, as they constantly strive to make optimal choices to achieve financial gains. A significant challenge facing investors involves data analysis, risk estimation, and potential gains. This is where the importance of mathematics comes into play. Mathematics is not just a theoretical science but a powerful tool that enables the analysis of information and the formulation of accurate conclusions. In the world of investment, mathematics can guide decisions and increase their precision. Whether you are trying to estimate the present value of a specific investment, analyze stocks, or manage an investment portfolio, mathematics equips you with powerful tools to make informed decisions. This research aims to explore the pivotal role played by mathematics in investment decision-making. We will examine how mathematical models and quantitative analysis are used to estimate value, manage risks, and enhance investment performance. Case studies and practical applications will be presented to illustrate how mathematics is employed in making smart investment decisions
󰠾
󰡴󰙿󰉅󰐃󰈉 󰠾󰠵
󰡮󰋦󰍜󰐃󰈉󰊦󰒰󰌏󰐃󰈉󰋅󰗎󰑔󰌏󰐃󰈉󰑡󰍜󰐜󰈓󰊀󰑡󰌎󰙿󰈰
󰠶
󰡣󰒰󰌎󰘍󰐃󰈉󰐘󰑸󰐊󰍔󰑧󰑡󰖌󰋔󰈓󰊒󰉅󰐃󰈉󰑧󰑡󰖭󰊶󰈓󰌰󰉅󰎙󰓶󰈉󰐘󰑸󰐊󰍜󰐃󰈉󰑡󰗎󰐊󰚠
󰑡󰖭󰊶󰈓󰌰󰉅󰎙󰓶󰈉󰐘󰑸󰐊󰍜󰐃󰈉󰐤󰌎󰎙
󰋔󰈉󰋦󰎞󰐃󰈉󰊷󰈓󰊔󰈰󰈉󰑡󰗎󰐊󰐠󰍔 󰠾󰠈
󰡻󰑡󰖭󰊶󰈓󰌰󰉅󰎙󰓶󰈉󰈛󰈓󰗎󰌫󰈓󰖌󰔢󰐊󰐃 󰠈󰠶
󰡭󰊒󰑔󰐃󰈉󰏼󰑧󰓴󰈉 󰠾󰠈
󰡯󰍀󰑸󰐃󰈉 󰠉
󰡼󰉅󰐊󰐠󰐃󰈉
󰐨󰈉󰑸󰐺󰍔
󰑡󰐊󰊂󰈉󰋅󰐠󰐃󰈉
󰊷󰈓󰊔󰈰󰈉 󰠾󰠈
󰡻󰈛󰈓󰗎󰌫󰈓󰖌󰔢󰐃󰈉󰋔󰑧󰊶󰒎󰋔󰈓󰐠󰉆󰘍󰌃󰓶󰈉󰋔󰈉󰋦󰎞󰐃󰈉
󰐃󰑡󰗎󰎞󰗎󰉄󰍄󰈰󰑡󰌃󰈉󰋔󰊶󰒎󰋔󰈓󰗎󰍜󰐠󰑃󰒟󰈓󰖹󰉅󰐃󰈉󰑧 󰠾󰠈
󰡵󰈓󰖌󰔢󰐃󰈉󰍤󰎙󰑸󰉅󰐃󰈉
The Role of Mathematics in Investment Decision-Making: An Applied Study
of Mathematical Expectation and Variance Criteria
󰊶󰌼󰋅󰐠󰊓󰐜󰑡󰗎󰊓󰖘󰈉󰑧󰋔
󰠾
󰡴󰙿󰉅󰐃󰈉 󰠾󰠵
󰡮󰋦󰍜󰐃󰈉󰊦󰒰󰌏󰐃󰈉󰋅󰗎󰑔󰌏󰐃󰈉󰑡󰍜󰐜󰈓󰊀󰑡󰌎󰙿󰈰
tebessa.dz-mohammed.rouabhia@univ
󰊶󰈇󰑡󰎀󰗎󰍄󰐃󰏼󰑸󰐊󰑔󰈯
󰠾
󰡴󰙿󰉅󰐃󰈉 󰠾󰠵
󰡮󰋦󰍜󰐃󰈉󰊦󰒰󰌏󰐃󰈉󰋅󰗎󰑔󰌏󰐃󰈉󰑡󰍜󰐜󰈓󰊀󰑡󰌎󰙿󰈰
tebessa.dz-latifa.bahloul@univ

         

.
   



           



       

Investment is a process of forecasting the future and making influential
decisions that carry both risks and opportunities. Investment decisions present
investors with challenges and opportunities they cannot ignore, as they constantly
strive to make optimal choices to achieve financial gains. A significant challenge
facing investors involves data analysis, risk estimation, and potential gains. This is
where the importance of mathematics comes into play.
Mathematics is not just a theoretical science but a powerful tool that enables
the analysis of information and the formulation of accurate conclusions. In the world
of investment, mathematics can guide decisions and increase their precision. Whether
you are trying to estimate the present value of a specific investment, analyze stocks, or
manage an investment portfolio, mathematics equips you with powerful tools to make
informed decisions.
This research aims to explore the pivotal role played by mathematics in
investment decision-making. We will examine how mathematical models and
quantitative analysis are used to estimate value, manage risks, and enhance
investment performance. Case studies and practical applications will be presented to
illustrate how mathematics is employed in making smart investment decisions.
Kaywords: Investment Risk Management Project Evaluation Return and Risk
Investment Decision Making Investment Investment Decision.




            
.
           
           








  
.






1

1 J.L Bailly et des autres , Macroéconomie , 2eme édition , Aubin imprimeur, paris , 2006, pp 101-102





1


    FBCF      

 QS    
        I= FBCF+DS  
           



2





3


            
            

 2









1 
2 
3 



1


 
   


.
 .2


2





 . 3

3









          
             


4





ردنأ ميلو فطاع 1
2  
3


4

           



              

1

 


     


2


              











3


DRDélai de Récupération



DR=I0/CF

I0

CF 

DR
DR
1
2
3
DR
TRC(Taux de Rendement Comptable
   
    

 TRC= RN'/I0*100
 RN'
I0


TRC



VAN (La Valeur Actuelle Nette




VAN = ΣCFi=1n (1+t) i+vR (1+t) -n -I0

VAN = CFi [(1-(1+t) -n) /t] -I0
CFivRI0

nt

VAN
 VAN          

VAN
 (Taux de Rentabilité Interne) TRI


1

TRIVAN
ΣCFi=1n (1+TRI) i+ vR (1+t) -n = I0
 TRI     
VAN1 t1VAN2t2

TRI = t1 + [VAN1/ (VAN1-VAN2)] * (t2-t1)
VAN1t1
VAN2t2
t1t2

-1 
.


     

1

IPIndex Profitability



IP = (ΣCFi=1n (1+t) -i) /I0
CFit I0
n

o  IP
o IP


 
         
VAN



EVANƩPiVAN
I0
Pi

 VAN
 VAN = ΣCFi=1n (1+t) i+vR (1+t) -n -I0
E(VAN)= (1+t) *E(CF1)]+….+ (1+t) n*E(CFn)]+ (1+t) n*E(VR)]- I0

o E(VAN)
o E(VAN)

           


2


VVAN= E(VAN^2)-[E(VAN)]^2
V(VAN)=∑i=1i=n(1+t)^-i*v(CFi)

1 - هسفن عجرملا ص ،16.
2 - 




1
P1P2
I0 : P1NI0 : P2N


P1
CF1
Pi
CF2
Pi
1
2
3
60
70
80
0.3
0.4
0.3
50
60
70
0.4
0.3
0.3


P2
CF1
Pi
CF2
Pi
1
2
3
30
62
90
0.3
0.4
0.3
50
80
100
0.4
0.4
0.2

182
230
P1P2

%VR CF


P1


P1
CF1
Pi CF1
P CF1^2
CF2
Pi
Pi CF2
P CF2^
1
2
3
60
70
80
18
28
24
1080
1960
1920
50
60
70
0.4
0.3
0.3
20
18
21
1000
1080
1470

70
4960
59
3550
-E(VAN)
E(VAN)= (1+t) *E(CF1)]+….+ (1+t) n*E(CFn)]+ (1+t) n*E(VR)]- I0

1 -

E(VAN)=[(1.1^-1)*(70)]+[(1.1^-2)*(59)]-100 =12.39 >0
V(VAN)
V(VAN)=i=1…i=n(1+t)^-i*v(CFi)
VVAN (1.1^-1)*[4960-(70^2)] + (1.1^-2)*[3550-(59^2)] = 111.59
P2


P2
CF1
Pi CF1
P CF1^
CF2
Pi CF2
P CF2^
1
2
3
30
62
90
09
24.8
27
270
1537.6
2430
50
80
100
20
32
20
1000
2560
2000

182
60.8
4237..6
230
72
5560
-E(VAN)
E(VAN)= (1+t) *E(CF1)]+….+ (1+t) n*E(CFn)]+ (1+t) n*E(VR)]- I0

E(VAN)=[(1.1^-1)*(60.8)]+[(1.1^-2)*(72)]-100 =14.77 >0
V(VAN)
V(VAN)=i=1…i=n(1+t)^-i*v(CFi)
VVAN (1.1^-1)*[4237.6-(60.8^2)] + (1.1^-2)*[5560-(72^2)] =802.52


       P2   

       P1  





           

         
           

  
 



 I






 









 II



-

 III





J.L Bailly et des autres , Macroéconomie , 2eme édition , Aubin imprimeur, paris ,
2006, pp 101-102
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