  This paper obtains an asymptotic formula for the finite-time ruin probability
of the compound nonhomogeneous Poisson risk model with a constant interest
force, in which the claims are conditionally independent random variables with
a common subexponential distribution. The paper also obtains some asymptotic
relations of randomly weighted sums $\sum_{i=1}^n \theta_iX_i$, in which the
weights $\theta_i$ $i=1,2,\cdots, n$ are positive random variables which are
bounded above and the primary random variables $X_i$, $i=1,2,\cdots,n$ are
conditionally independent and follow subexponential distributions.
