  We study investment and insurance demand decisions for an agent in a
theoretical continuous-time expected utility maximization model that combines
risky assets with an (exogenous) insurable background risk. This risk takes the
form of a jump-diffusion process with negative jumps in the return rate of the
(self-financed) wealth. The main distinctive feature of our model is that the
agent's decision on portfolio choice and insurance demand causes nonlinear
friction in the dynamics of the wealth process. We use the dynamic programming
approach to find optimality conditions under which the agent assumes the
insurable risk entirely, or partially, or purchases total insurance against it.
In particular, we consider differential and piece-wise linear portfolio
allocation frictions, with differential borrowing and lending rates as our most
emblematic example. Finally, we present a mutual-fund separation result and
illustrate our results with several numerical examples when the adverse jump
risk has Beta distribution.
