  The optimal stopping problem for the risk process with interests rates and
when claims are covered immediately is considered. An insurance company
receives premiums and pays out claims which have occured according to a renewal
process and which have been recognized by them. The capital of the company is
invested at interest rate $\alpha\in\Re^{+}$, the size of claims increase at
rate $\beta\in\Re^{+}$ according to inflation process. The immediate payment of
claims decreases the company investment by rate $\alpha_1$. The aim is to find
the stopping time which maximizes the capital of the company. The improvement
to the known models by taking into account different scheme of claims payment
and the possibility of rejection of the request by the insurance company is
made. It leads to essentially new risk process and the solution of optimal
stopping problem is different.
