Polynomial affine approach to HARA utility maximization with applications to OrnsteinUhlenbeck 4/2 models.

Highlights：

• A high level of accuracy of the methodology and low computational time for 35-dimensional multivariate stochastic covariance models.

• Theoretical cases were solutions either do not exist or are not unique are explored numerically with excellent results for the methodology.

• The optimal strategy, optimal wealth and value function are numerically studied for an OU 4/2 model. The analysis confirms substantial changes in allocations due to relatively small changes in model parameters.

• An efficient frontier of pre-commitment strategies for dynamic MVT is obtained.

• The suboptimality of myopic strategies in terms of the certainty equivalent rate (CER), for OU 4/2 models, is corroborated. It confirms low CERs for investors ignoring stochastic volatility (SV), to the point that a myopic strategy may be preferable to a strategy that neglects SV.

摘要

•A numerical method to approximate optimal allocation and value function for a risk-averse investor in a general HARA setting, which includes expected utility (EUT) and mean-variance (MVT) theories.•A high level of accuracy of the methodology and low computational time for 35-dimensional multivariate stochastic covariance models.•Theoretical cases were solutions either do not exist or are not unique are explored numerically with excellent results for the methodology.•The optimal strategy, optimal wealth and value function are numerically studied for an OU 4/2 model. The analysis confirms substantial changes in allocations due to relatively small changes in model parameters.•An efficient frontier of pre-commitment strategies for dynamic MVT is obtained.•The suboptimality of myopic strategies in terms of the certainty equivalent rate (CER), for OU 4/2 models, is corroborated. It confirms low CERs for investors ignoring stochastic volatility (SV), to the point that a myopic strategy may be preferable to a strategy that neglects SV.