Partial Differential Equations in Economics and Finance

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Nova Publishers, 2007 - Mathematics - 134 pages
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This book reviews the basic theory of partial differential equations of the first and second order and discusses their applications in economics and finance. It starts with well-known applications to consumer and producer theory, and to the theory of option pricing and then introduces new applications that emerge from current research (some of which is the author's own) in bounded rationality, game theory, and multi-dimensional screening.
 

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Contents

Partial Differential Equations
5
111 Examples
6
12 The Complete Integral the General Integral and the Singular Integral
8
121 Compatible Systems of the First Order PDEs
9
13 The Second Order Partial Differential Equations
10
132 Boundary Value Problems for Elliptic Equations
11
133 The Cauchy Problem for a Parabolic Equation
13
134 Examples
15
613 A Discussion of One Experiment
56
614 Conclusions
60
62 A Model of Social Learning
61
63 Locally Improving Adjustment Rules and the Deduced Utility
64
64 Estimating the Utility Function from the Data
71
65 Evolutionary Determination of Adjustment Rules
72
66 A Note of Caution
73
68 The Optimal Monopoly Pricing Under Viscous Demand and Customers Turnover
76

14 Exercises
18
15 Bibliographic Notes
19
Stochastic Processes
21
22 The Generator of the Stochastic Process
22
23 Exercises
24
24 Bibliographic Notes
25
Economic Applications
27
Consumer Theory
31
32 Finding the Indirect Utility from the Marshallian Demand
33
33 An Example of Finding the Indirect Utility Function from the Demand
34
34 Exercises
36
35 Bibliographic Notes
37
Producer Theory
39
42 The Main Partial Differential Equation of the Production Theory
40
43 Examples Solved
41
44 Exercises
44
Pricing of the Financial Derivatives
45
52 The Fundamental Equation of Derivatives Pricing
47
53 Pricing of European Options
48
54 Financial Markets and Bounded Rationality
49
A Theory of Boundedly Rational Behavior
51
61 A Model of Noisy Individual Adjustment
53
612 The Multidimensional Case
55
681 The Model
78
682 The Population Turnover Rate and the Monopolists Profits
81
683 Conclusions
82
610 Exercises
83
611 Bibliographic Notes
84
Game Theory
85
72 An Evolutionary Model of Reciprocity
86
721 The Model
89
Replicator Dynamics with Migration
93
731 The Model
97
732 Some Examples
106
733 The Behavioral Foundations of the Model
110
734 Discussion and Conclusions
113
74 Exercises
114
The Multidimensional Screening Model
117
81 Hamiltonian Approach and the First Order Conditions
118
82 An Example
120
83 Conclusions
121
84 Exercises
122
Conclusions
123
References
125
Index
133
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