Cap the insurance payout at I, and then maximize over I allowing p to equal d D) (1-m)U(Y-p-d)+m(1-p)U(Y-z+1 +ad (r(d)(U(Y-p7-d-U(Y-z+1-p7-a) 1-)U(Y-p-d)-U(Y-Z+1-p1-d) a(1-)(-()U(Y-p7-d)+ od r(I'(dDU(Y-Z+I-pI-d) At the point where this is equal to zero you have an optimal Insurance capCap the insurance payout at I, and then maximize over I allowing p to equal dI 1  pU Y  pI  d  1  pUY  Z  I   d I  dUY  pI  d  UY  Z  I  pI  d  1  UY  pI  d  UY  Z  I  pI  d d I 1   dIU Y  pI  d  d I  dIU Y  Z  I  pI  d At the point where this is equal to zero, you have an optimal insurance cap