  A usual reinsurance policy for insurance companies admits one or two layers
of the payment deductions. Under optimal criterion of minimizing the
conditional tail expectation (CTE) risk measure of the insurer's total risk,
this article generalized an optimal stop-loss reinsurance policy to an optimal
multi-layer reinsurance policy. To achieve such optimal multi-layer reinsurance
policy, this article starts from a given optimal stop-loss reinsurance policy
$f(\cdot).$ In the first step, it cuts down an interval $[0,\infty)$ into two
intervals $[0,M_1)$ and $[M_1,\infty).$ By shifting the origin of Cartesian
coordinate system to $(M_{1},f(M_{1})),$ and showing that under the $CTE$
criteria $f(x)I_{[0, M_1)}(x)+(f(M_1)+f(x-M_1))I_{[M_1,\infty)}(x)$ is, again,
an optimal policy. This extension procedure can be repeated to obtain an
optimal k-layer reinsurance policy. Finally, unknown parameters of the optimal
multi-layer reinsurance policy are estimated using some additional appropriate
criteria. Three simulation-based studies have been conducted to demonstrate:
({\bf 1}) The practical applications of our findings and ({\bf 2}) How one may
employ other appropriate criteria to estimate unknown parameters of an optimal
multi-layer contract. The multi-layer reinsurance policy, similar to the
original stop-loss reinsurance policy is optimal, in a same sense. Moreover it
has some other optimal criteria which the original policy does not have. Under
optimal criterion of minimizing general translative and monotone risk measure
$\rho(\cdot)$ of {\it either} the insurer's total risk {\it or} both the
insurer's and the reinsurer's total risks, this article (in its discussion)
also extends a given optimal reinsurance contract $f(\cdot)$ to a multi-layer
and continuous reinsurance policy.
