  We consider the problem of optimal investment and consumption in a class of
multidimensional jump-diffusion models in which asset prices are subject to
mutually exciting jump processes. This captures a type of contagion where each
downward jump in an asset's price results in increased likelihood of further
jumps, both in that asset and in the other assets. We solve in closed-form the
dynamic consumption-investment problem of a log-utility investor in such a
contagion model, prove a theorem verifying its optimality and discuss features
of the solution, including flight-to-quality. The exponential and power utility
investors are also considered: in these cases, the optimal strategy can be
characterized as a distortion of the strategy of a corresponding non-contagion
investor.
