Expression 5: "f" Subscript, 1 , Baseline left parenthesis, "v" , right parenthesis equals "F" Subscript, 1 , Baseline prime left parenthesis, "v" , right parenthesisf1v=F1′v
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Expression 6: "w" Subscript, 1 , Baseline left parenthesis, "v" , right parenthesis equals "v" minus StartFraction, left parenthesis, 1 minus "F" Subscript, 1 , Baseline left parenthesis, "v" , right parenthesis , right parenthesis Over "f" Subscript, 1 , Baseline left parenthesis, "v" , right parenthesis , EndFractionw1v=v−1−F1vf1v
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Valuation is distributed *normally* with mean a and std b:
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Expression 8: "f" Subscript, 2 , Baseline left parenthesis, "v" , right parenthesis equals StartFraction, 1 Over "b" StartRoot, 2 pi , EndRoot , EndFraction "e" Superscript, negative StartFraction, left parenthesis, "v" minus "a" , right parenthesis squared Over 2 "b" squared , EndFraction , Baseline left brace, "a" minus 5 "b" less than or equal to "v" less than or equal to "a" plus 5 "b" , right bracef2v=1b2πe−v−a22b2a−5b≤v≤a+5b
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Expression 9: "F" Subscript, 2 , Baseline left parenthesis, "v" , right parenthesis equals Start integral from "a" minus 5 "b" to "v" , end integral, "f" Subscript, 2 , Baseline left parenthesis, "x" , right parenthesis "d" "x" left brace, "a" minus 5 "b" less than or equal to "v" less than or equal to "a" plus 5 "b" , right braceF2v=∫va−5bf2xdxa−5b≤v≤a+5b
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Expression 10: "w" Subscript, 2 , Baseline left parenthesis, "v" , right parenthesis equals "v" minus StartFraction, left parenthesis, 1 minus "F" Subscript, 2 , Baseline left parenthesis, "v" , right parenthesis , right parenthesis Over "f" Subscript, 2 , Baseline left parenthesis, "v" , right parenthesis , EndFraction left brace, "a" minus 5 "b" less than or equal to "v" less than or equal to "a" plus 5 "b" , right bracew2v=v−1−F2vf2va−5b≤v≤a+5b