Junji Ishikawa

The aim of the lecture

Since accounting system is a kind of information systems, the fundamental theory of how to calculate and compare the value of information systems is essential for studying the foundation of accounting information systems.

In this lecture, we learn the foundation of the valuation of information systems by focusing on the quantity and the value of uncertainty/ information (Part �T) and sharing and dispersion of uncertainty (Part �U).




The contents of the lecture

Part �T

1)Calculation of the value of information systems

2)Comparability of the value of information systems

3)Economic choice and the cost of uncertainty

4)Strict uncertainty and the value of information

5)Entropy and the quantity of uncertainty/ information

Part �U

6)Sharing and Dispersion of Uncertainty

7)Risk dispersion and risk hedge

8)Agency theory and the value of information

9)Game theory and the value of information













Overview of the Lecture





Mathematical Analysis of Information Value

English version (condensation) of my book

Junji Ishikawa





1 The Value of Information Systems

1.1 How to calculate the value of information systems (1): numerical example 1.1

1.2 How to calculate the value of information systems (2): numerical example 1.2

1.3 Improvement of accuracy and the value of information systems: numerical example 1.3

1.4 Change of experience/ knowledge and the value of information systems: numerical example 1.4

1.5 The value of the ultimate information system: numerical example 1.5

Appendix 1.1 General explanation

Appendix 1.2 Baye’s theorem and the expected value of information systems




2 Comparability of the Value of Information Systems

2.1 How to compare the value of formation systems: numerical example 2.1

2.2 Conditions of comparability: numerical example 2.2

2.3 The value of sample information systems: numerical example 2.3

2.4 Comparability of the direct sum type of information systems: numerical example 2.4




3 Valuation of Uncertainty and the Value of Information Systems

3.1 The expected value of perfect information system and valuation of uncertainty: numerical example 3.1

3.2 Dual valuation of uncertainty: numerical example 3.2

3.3 Risk avoidance and the expected value of perfect information system: numerical example 3.3

3.4 Risk avoidance and the cost of uncertainty: numerical example 3.4

Appendix3.1 Certainty monetary equivalence and risk premium




4 Strict Uncertainty and the Value of Information Systems

4.1 Newsboy problems or Christmas tree problems: numerical example 4.1

4.2 Two types of opportunity loss and the dilemma between them

: numerical example 4.2

4.3 Min.Max optimal behavior and Min.Max equilibrium: 〃

4.4 The choice and the cost of uncertainty: numerical example 4.3

4.5 The value of information under strict uncertainty: 〃

Appendix 4.1 Optimal behavior and two types of opportunity loss under risk situation

Appendix 4.2 The value of information under strict uncertainty




5.The Quantity and the Cost of Uncertainty

5.1 The quantity of uncertainty and entropy: numerical example 5.1

5.2 Entropy and the quantity of information: numerical example 5.2

5.3 The quantity of information and its non-negativity (Shannon’s inequality)<

5.4 The value of information and its non- negativity

5.5 The decomposition of the cost of uncertainty (1)

5.6 The decomposition of the cost of uncertainty (2)

Appendix 5.1 The relationship between prior distribution and posterior distribution

Appendix 5.2 Equivalence between two approaches

　




6.Sharing and Dispersion of Uncertainty

6.1 Uncertainty and institution

6.2 Joint incentive and risk allocation: numerical example 6.1

6.3 The power of negotiation and prediction and risk allocation

: numerical example 6.2

6.4 Group decision and risk attitude: numerical example 6.3

6.5 Uncertainty and organizations

Appendix 6.1 Pareto optimal risk allocation

Appendix 6.2 Group exponential function