  We study the asymptotic behavior of ruin probabilities, as the initial
reserve goes to infinity, for a reserve process model where claims arrive
according to a renewal process, while between the claim times the process has
the dynamics of geometric Brownian motion-type It\^o processes with
time-dependent random coefficients. These coefficients are ``reset" after each
claim time, switching to new values independent of the past history of the
process. We use the implicit renewal theory to obtain power-function bounds for
the eventual ruin probability. In the special case when the random drift and
diffusion coefficients of the investment returns process remain unchanged
between consecutive claim arrivals, we obtain conditions for existence of
Lundberg's exponent for our model ensuring the power function behaviour for the
ruin probability.
