  We study the optimal investment and proportional reinsurance problem of an
insurance company, whose investment preferences are described via a forward
dynamic utility of exponential type in a stochastic factor model allowing for a
possible dependence between the financial and insurance markets. Specifically,
we assume that the asset price process dynamics and the claim arrival intensity
are both affected by a common stochastic process and we account for a possible
environmental contagion effect through the non-zero correlation parameter
between the underlying Brownian motions driving the asset price process and the
stochastic factor dynamics. By stochastic control techniques, we construct a
forward dynamic exponential utility, and we characterize the optimal investment
and reinsurance strategy. Moreover, we investigate in detail the
zero-volatility case and provide a comparison analysis with classical results
in an analogous setting under backward utility preferences. We also discuss an
extension of the conditional certainty equivalent. Finally, we perform a
numerical analysis to highlight some features of the optimal strategy.
