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Operating in a competitive insurance market, the \ insurance company sets its premium rate r to breakeven in expectation. In \ other words, under the premium rate r that it offers, the insurance company\ \[CloseCurlyQuote]s expected profit,", StyleBox["r(\[Alpha] p+cs+f)", FontColor->RGBColor[1, 0, 0]], ", equals the expected coverage \n", StyleBox["(1-e) (\[Alpha] p+cs+f).", FontColor->RGBColor[1, 0, 0]], "\nSubstituting e given in", Cell[BoxData[ StyleBox[ RowBox[{"e", ":=", FractionBox[ RowBox[{ RowBox[{"p", RowBox[{"(", RowBox[{"1", "-", " ", "\[Alpha]"}], ")"}]}], "+", "\[Theta]"}], RowBox[{"2", " ", SuperscriptBox["k", "B"]}]]}], FontColor->RGBColor[1, 0, 0]]], CellChangeTimes->{{3.847072090450409*^9, 3.847072097890996*^9}, { 3.847074047134727*^9, 3.847074085951888*^9}},ExpressionUUID-> "c21b5710-5241-4d7c-ba46-cfaf817fc9ea"], " , the insurance company breakeven condition can be satisfied if and only \ if", StyleBox[" p \[GreaterEqual] ", FontColor->RGBColor[1, 0, 0]], Cell[BoxData[ FormBox[ SuperscriptBox["p", "IA"], TraditionalForm]], FontColor->RGBColor[1, 0, 0],ExpressionUUID-> "68d7423d-59f2-490e-a9c2-f7ef15d52475"], StyleBox[" \[Congruent]", FontColor->RGBColor[1, 0, 0]], Cell[BoxData[ FractionBox[ RowBox[{ RowBox[{"2", " ", RowBox[{"k", "^", "B"}], " ", RowBox[{"(", RowBox[{"1", "-", "r"}], ")"}]}], "-", " ", "\[Theta]"}], RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], " "}]]], CellChangeTimes->{3.8470757908903217`*^9}, FontColor->RGBColor[1, 0, 0],ExpressionUUID-> "c968a0f2-71fa-480e-b3be-65f924a3b294"], " ,which we refer as the ", StyleBox["insurance company\[CloseCurlyQuote]s underwriting constraint", FontColor->RGBColor[1, 0, 0]], ". 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