Estimation, Evaluation, and Selection of Actuarial Models
Estimation, Evaluation, and Selection of Actuarial Models Estimation, Evaluation, and Selection of Actuarial Models
134 APPENDIX B. USING MICROSOFT EXCEL TM The reason adding the constraints is not needed here is that the solution Solver finds meets the constraints anyway. Clicking on “Options” brings up the following dialog box: I have made two changes from the default settings. The “Use Automatic Scaling” box has been checked. This improves performance when the parameters are on different scales (as is the case here). Also, “Central” approximate derivatives have been selected. Additional precision in the answer can be obtained by making the Precision, Tolerance, and Convergence numbers smaller. Clicking OK on the options box (no changes will be apparent in the Solver box) and then clicking “Solve” results in the following:
135 Clicking OK gives the answer. Users of Solver (or any numerical analysis routine) should always be wary of the results. The program may announce a solution when the maximum has not been found and it may give up when there is a maximum to be found. When the program gives up, it may be necessary to provide better starting values. To verify that an announced solution is legitimate (or at least is a local maximum), it is a good idea to check the function at nearby points to see that the values are indeed smaller. In addition to maximizing and minimizing functions of several variables, Solver can also solve equations. By choosing the “Value of:” radio button in the Solver dialog box a value can be entered and then Solver will manipulate the By Changing Cells in order to set the contents of the Target Cell equal to that value. If there is more than one function, the constraints can be used to set them up. The following spreadsheet and Solver dialog box are set up to solve the two equations x + y =10and x −y =4with starting values x =8and y =5(to illustrate that the starting values do not have to be solutions to any of the equations).
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134 APPENDIX B. USING MICROSOFT EXCEL TM<br />
The reason adding the constraints is not needed here is that the solution Solver finds meets the<br />
constraints anyway. Clicking on “Options” brings up the following dialog box:<br />
I have made two changes from the default settings. The “Use Automatic Scaling” box has been<br />
checked. This improves performance when the parameters are on different scales (as is the case<br />
here). Also, “Central” approximate derivatives have been selected. Additional precision in the<br />
answer can be obtained by making the Precision, Tolerance, <strong>and</strong> Convergence numbers smaller.<br />
Clicking OK on the options box (no changes will be apparent in the Solver box) <strong>and</strong> then clicking<br />
“Solve” results in the following:
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