### Table 10 Unrestricted LA/AIDS Approximate Exact Approximate Exact

"... In PAGE 21: ... The results indicate the following: The approximate price changes can be a very poor guide relative to exact price changes. The numbers in parentheses are the common number of approximate and exact price increases which are statistically different from zero or whose 90% confidence interval Insert Table10 Here Table 10: Unrestricted LA/AIDS Price Simulations... In PAGE 21: ... The results indicate the following: The approximate price changes can be a very poor guide relative to exact price changes. The numbers in parentheses are the common number of approximate and exact price increases which are statistically different from zero or whose 90% confidence interval Insert Table 10 Here Table10 : Unrestricted LA/AIDS Price Simulations... ..."

### Table 5: Investment Example with 10% Interest We will determine W by nding state prices. The argument is exactly as before. We solve the equations

### Table 12: Summary of Price Simulations

"... In PAGE 21: ... Prices changes that are statistically significant at the 5 and 10% level, based on t-tests, are also indicated. Table12 summarizes the findings regarding the price changes. The results indicate the following: The approximate price changes can be a very poor guide relative to exact price changes.... ..."

### Table 6: Investment Example with 10% Interest and 20% Rate of Return Given the price of the investment, we can proceed exactly as in Sections 4.2 and 5.1 to nd the state prices. Unlike the previous analysis, we now obtain di erent values for the prices in the two states: 1 = :3636 and 2 = :5455:

### Table 8 Unrestricted Rotterdam Approximate Exact Approximate Exact

"... In PAGE 21: ...Table8 Here Table 8: Unrestricted Rotterdam Price Simulations Insert Table 9 Here Table 9: Restricted Rotterdam Price Simulations 5.2.... In PAGE 21: ... Table8 : Unrestricted Rotterdam Price Simulations Insert Table 9 Here Table 9: Restricted Rotterdam Price Simulations 5.2.... ..."

### Table 9 Restricted Rotterdam Approximate Exact Approximate Exact

"... In PAGE 21: ...Table 8: Unrestricted Rotterdam Price Simulations Insert Table9 Here Table 9: Restricted Rotterdam Price Simulations 5.2.... In PAGE 21: ...Table 8: Unrestricted Rotterdam Price Simulations Insert Table 9 Here Table9 : Restricted Rotterdam Price Simulations 5.2.... ..."

### Table 11 Restricted LA/AIDS Approximate Exact Approximate Exact

"... In PAGE 22: ...Table11 Here Table 11: Restricted LA/AIDS Price Simulations excludes 0. The extent of overlap is not very large, indicating that the approximate methodology is prone to being both under and over inclusive.... In PAGE 22: ... Table11 : Restricted LA/AIDS Price Simulations excludes 0. The extent of overlap is not very large, indicating that the approximate methodology is prone to being both under and over inclusive.... ..."

### Table 10. Comparison of actual cocoa put option prices at the New York Board of Trade and actuarially fair insurance premiums from model for three months ahead. All prices expressed as shares of future prices)

"... In PAGE 22: ... The estimated actuarially fair premiums are generally smaller than the market determined put option prices. Table10 compares for illustration the prices of cocoa put options in the New York Board of Trade (NYBOT) in June 5, 2002, February 2, 2001, and April 4, 2000, for three month maturities, and different strike prices and compares them with the actuarially fair insurance premiums calculated with the formulas here, for the exact same deviations of strike prices from future prices as the ones actually observed in the market. Table 11 does the same for two and five month put options and for different dates12.... ..."

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### Table 2 Comparison of Branch-and-Cut and Branch-and-Price Results on CPPMIN Type I Problems for S = 4 it takes a long time to compute. The basic trends and analysis are exactly the same as those for Type I data. For detailed results, see [14].

2005

"... In PAGE 20: ...problem as an IP is not very big, considering that these pricing problems are NP hard problems, solving them repeatedly sums up to a considerable amount of time. To compare the branch-and-cut method in Ji and Mitchell [15] with the branch-and-price-and-cut method presented in this paper, we put together Table2 with the data from Table 2 in [15] and Table 1. For comparison con- venience, we have adjusted the reported time for \B amp;C run quot; to represent the total computation time, i.... In PAGE 20: ...otal computation time, i.e. it includes root node time. The \B amp;C run quot; time in Table2 in [15] does not include the root node time. By comparing the performance in terms of both gap and time, one can see that branch-and-price-and-cut outperforms branch-and-cut, on instances with no more than 43 vertices.... ..."

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### Table 4 Number of solved pricing problems.

2004

"... In PAGE 25: ...ave been solved to proven optimality. The run-time is 160.68s on average, which is the fastest of our four B amp;P variants. In Table4 , the total number of pricing problems solved in each class and their sums are given for the B amp;P approaches. Furthermore, the bar charts shown in Fig.... In PAGE 29: ...Table4 we can observe that when using FFBC only (BPNoR) the number of solved pricing problems is lower than the one of BP where CPLEX(restricted 3-stage 2DKP) is used. Pricing using a more sophisticated heuristic, in this case exactly solving restricted 3-stage 2DKP, can therefore improve the overall results, see also Table 3.... In PAGE 29: ... These pricing problems can be denoted as easy ones. Looking at absolute numbers shows that CPLEX(restricted 3-stage 2DKP) successfully solved 21 500 pricing problems, which approximately corresponds to the increase of solved pricing problems when comparing BPNoR to BP in Table4 . The bar charts showing the relative success rates of the pric- ing algorithms indicate that the absolute number of easy pricing problems roughly remained the same.... ..."

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