Optimal Reciprocal Reinsurance under VaR or TVaR Constraint.

Step 1: Find HT <math overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><msup><mrow><mi>I</mi></mrow><mrow><mo>*</mo></mrow></msup><mfenced close=")" open="("><mrow><mi>x</mi></mrow></mfenced><mo>=</mo><msub><mrow><mi mathvariant="normal">arg min</mi></mrow><mrow><mi>I</mi><mrow><mo stretchy="false">(</mo><mrow><mi>x</mi></mrow><mo stretchy="false">)</mo></mrow><mo> </mo><msub><mrow><mi mathvariant="script">F</mi></mrow><mrow><mtext>R</mtext></mrow></msub></mrow></msub><mfenced close="|" open="|"><mrow><mi>I</mi><mfenced close=")" open="("><mrow><mi>x</mi></mrow></mfenced><mo>-</mo><mrow><mover accent="true"><mrow><mi>I</mi></mrow><mo stretchy="false"> </mo></mover></mrow><mfenced close=")" open="("><mrow><mi>x</mi></mrow></mfenced></mrow></mfenced></math> ht . Additionally, the notation HT <math overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced close=")" open="("><mi>x</mi><mo>-</mo><mi>A</mi></mfenced><mo>+</mo></msup><mo> </mo><mi>max</mi><mfenced close="}" open="{"><mi>x</mi><mo>-</mo><mi>A</mi><mo>,</mo><mn>0</mn></mfenced></math> ht . Step 2: Verify HT <math overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><msup><mrow><mi>I</mi></mrow><mrow><mo>*</mo></mrow></msup><mfenced close=")" open="("><mrow><mi>x</mi></mrow></mfenced><mo> </mo><msub><mrow><mi mathvariant="script">I</mi></mrow><mrow><mtext>R</mtext></mrow></msub></math> ht . [Extracted from the article]