
New Results.
Solution & Explanation of Problems & Paradoxes
Contents
(in new windows)
1. Solution of Problems (of St. Petersburg Paradox of Allais Paradox of Equity Premium Puzzle of Risk Aversion of Gains and Losses of Loss Aversion of Overweighting of low Probabilities of Underweighting of high Probabilities of "FourFoldPattern" of Shape of Probability Weighting Function of Ellsberg Paradox of Preference Reversals ) 2. New Results ( "Impossibilities" in Forecasting "Necessities" in Planning )

1. Solution & Explanation
of Problems & Paradoxes
Solution & Explanation
of the FourFoldPattern The welldetermined facts are: For positive (gains) risky prospects, people typically 1) overweight low probabilities but 2) underweight high probabilities. For negative (losses) risky prospects, people typically 3) underweight low probabilities but 4) overweight high probabilities. Denoting the real value of probability, which value is near 100% as P_{high real} , the (positive) value of gain as G and the (negative) value of loss as G , we obtain P_{high real} < P_{high planned} and G * P_{high real} < G * P_{high planned} G * P_{high real} > G * P_{high planned} 2) the underweight of high probabilities gains and 4) the overweight of high probabilities losses. "Low probabilities can increase" does not mean they will necessarily increase. But this is a sufficient reason to prefer low probabilities in the state of equilibrium. Denoting the real value of probability, which value is near 0% as P_{low real} we obtain P_{low real possible} > P_{low planned} and G * P_{low real possible} > G * P_{low planned} G * P_{low real possible} < G * P_{low planned} 1) the overweight of low probabilities gains and 3) the underweight of low probabilities losses. Thus, the above facts can be explained naturally and uniformly. Top

2. New Results
"Impossibilities" in Forecasting
Possible conclusions from the first consequence of the principle: "Absolutely exact extrapolation forecasting is impossible" "Exact middlerange extrapolation forecasting is unattainable" Possible conclusions from the first and second consequences of the principle: "Absolutely reliable extrapolation forecasting is impossible" "Exact longrange extrapolation forecasting is impossible" "Quantitative extralongrange extrapolation forecasting is impossible" (Growing quantitative uncertainties and unforeseen events may modify an essential parameter for more than 50% from its maximal value) Possible conclusion from the second consequence of the principle: "Complete qualitative extralongrange extrapolation forecasting is impossible" (Unforeseen events may add an unforeseen qualitative feature in a complete picture)
"Necessities" in Planning
Possible conclusions from the principle in the scope of the concept "Future as the extrapolated Present": "Future is Modifications and Changes" "Shortterm and Mediumterm Planning is Necessary to be Flexible" "The Necessary Features of Longterm Planning should be Robustness & Resourcefulness" Top


