  In this paper the authors study a model for the optimal operation of a bank
or insurance company which was recently introduced by Peura and Keppo. The
model generalizes a previous one of Milne and Robertson by allowing the bank to
raise capital as well as to pay out dividends. Optimal operation of the bank is
determined by solving an optimal control problem. In this paper it is shown
that the solution of the optimal control problem proposed by Peura and Keppo
exists for all values of the parameters and is unique.
