Decision Theory Intro

Decision Theory Intro - Prof Dr Reinhard H Schmidt Decision...

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1 Decision Theory Prof. Dr. Reinhard H. Schmidt © Reinhard H. Schmidt Finance Department Goethe-University Frankfurt/Main Spring Term 2009 Lecture 2: Decisions under Certainty 21 April 2009 Master of Money and Finance
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2 Today‘s Lecture Basics for decisions under certainty with (only) one target value Decisions in the presence of multiple target values - The procedure of stepwise transformation - Substitute and supplementary preocedures Practical aspects of decision making under certainty © Reinhard H. Schmidt
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3 Decisions under Certainty and Formalism – The case of one single bjective Prof. Dr. Reinhard H. Schmidt
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4 Decision model under Certainty with one target value A i E i A 1 E 1 A 2 E 2 A 3 E 3 A n E n A=(A 1 ,…,A n ) : Alternatives E=(E 1 ,…,E n ) : Outcomes A  → Φ + Φ (A) : Preference function ‚Decision Field‘ ‚Target System‘
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5 Preference Relations The elementary operation in the theory of rational decision-making (TRD) is the pairwise comparison of objects of choice, establishing a preference relation over these objects; E i ‘s (A i ‘s). Basic preference relations: Strong preference E i > E j E i is ‚better‘ than E j . Weak preference E i ≥ E j E i is ‚at least good‘ as E j . Equivalence E i ≥ E j and E j ≥ E E i = E j E i and E j are equivalent Regarding such preference relations, the TRD postulates certain simple axioms (no proof required)
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6 (A1) Ordering Axiom A decision-maker X can state a preference relation for each pair of choice variables. There is no „incomparability“! Either E i > E j : X prefers E i over of E j. Or E i < E j : X prefers E j over E i. Or E i = E j : X is indifferent between E i and E j. Why do we make such an assumption? The TRD covers only formal rationality, requiring the existence of this elementary preference relation from any “rational” decision maker.
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7 (A2) Transitivity Axiom For any E i , E j , and E k : E i > E j and E j > E k E i > E k E i = E j and E j = E k E i = E k E i > E j and E j = E k E i > E k This means that if decision maker x is rational and prefers E i over E j and prefers E j over E k , than x also prefers E i over E k. This is the second fundamental rationality axiom. It follows from a fundamental economic principle called “no arbitrage principle
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8 No Arbitrage Principle Example 2a: Consider Sam‘s preference relations being as follows: Banana > Apple und Apple > Peach and Peach > Banana and suppose, more specifically, the following; Banana = Apple + 1 Euro Apple = Peach + 1 Euro Peach = Banana + 1 Euro Let‘s assume Sam has 1 B und 3 Euros, and Dirk has 1 P and 1 A. What would happen if they came to trade with Sam acting to preserve value for himself.
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9 Example 2a (Cont‘d) - Dirk offers Sam 1 P against 1 B + 1 Dollar. Sam accepts. - Dirk offers Sam 1 A against 1 P + 1 Dollar. Sam accepts.
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This note was uploaded on 06/12/2011 for the course ECON 101 taught by Professor Schmidt during the Spring '09 term at Uni Frankfurt.

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Decision Theory Intro - Prof Dr Reinhard H Schmidt Decision...

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