  We study a continuous-time asset-allocation problem for an insurance firm
that backs up liabilities from multiple non-life business lines with
underwriting profits and investment income. The insurance risks are captured
via a multidimensional jump-diffusion process with a multivariate compound
Poisson process with dependent components, which allows to model claims that
occur in different lines simultaneously. Using Lagrangian convex duality
techniques, we provide a general verification-type result for
investment-underwriting strategies that maximize expected utility from the
dividend payout rate and final wealth over a finite-time horizon. We also study
the precautionary effect on earnings retention of risk aversion, prudence,
portfolio constraints and multivariate insurance risk. We find an explicit
characterization of optimal strategies under CRRA preferences. Numerical
results for two-dimensional examples with policy limits illustrate the impact
of co-integration for ALM with multiple (dependent and independent) sources of
insurance risk.
