Optimal consumption and investment in general affine GARCH models

Our paper presents the first optimal analytical solution for an investor maximizing both consumption and terminal wealth within expected utility theory in the realm of GARCH models. Working in a general family of affine GARCH models, we derive an affine GARCH optimal wealth process, providing analytical representations for optimal allocation, consumption and value functions. In particular, the optimal consumption ratio avoids the undesirable scenario of investors consuming all wealth prior to maturity. Our numerical study highlights the importance of formally accounting for consumption as it disrupts the level of optimal risky allocations. It also shows a larger impact of stochastic conditional variance (heteroscedasticity) on risky allocations in comparison to the impact of non-Gaussianity. We find, in a numerical study based on S&P 500 index data over a 5-years horizon, that an investor following a Gaussian GARCH strategy can achieve 10% more total consumption and at the same time 8% more terminal wealth than another investor following a constant variance (homoscedastic) strategy.