Diffusion approximations for periodically arriving expert opinions in a financial market with Gaussian drift

Power Utility Maximization with Expert Opinions at Fixed Arrival Times in a Market with Hidden Gaussian Drift

“…In Subsecs. 4.1 and 7.4 we show that based on this model and on the diffusion approximations provided in [34] one can find efficient approximative solutions to utility maximization problems for partially informed investors observing high-frequency discrete-time expert opinions.…”

“…In addition to expert opinions arriving at discrete time points we will also consider expert opinions arriving continuously over time as in Davis and Lleo [11,12] who called this approach "Black-Litterman in Continuous Time". This is motivated by the results of Sass et al [33,34] who show that asymptotically as the arrival frequency tends to infinity and the expert's variance Γ grows linearly in that frequency the information drawn from these expert opinions is essentially the same as the information one gets from observing yet another diffusion process. This diffusion process can then be interpreted as an expert who gives a continuous-time estimation about the current state of the drift.…”

“…We model a financial market with one risk-free and multiple risky assets. The setting is based on Gabih et al [18,19] and Sass et al [32][33][34]. For a fixed date T > 0 representing the investment horizon, we work on a filtered probability space (Ω, G, G, P), with filtration G = (G t ) t∈[0,T ] satisfying the usual conditions.…”

“…For the literature on BLCT in which expert opinions are included we refer to a series of papers [18,19,[32][33][34] of the present authors and of Sass and Westphal. They investigate utility maximization problems for investors with logarithmic preferences in market models with a hidden Gaussian drift process and discrete-time expert opinions.…”

“…While for continuous-time expert opinions results are available from the work of Davis and Lleo, see [11][12][13], the case of discretetime expert opinions was only considered in the PhD of Kondakji [22] on which this paper is based. Recently, a few results of [22] were briefly mentioned in Sass et al [34] and applied in numerical experiments. Our main results are presented in Theorems 6.1 and 6.3 where we derive a backward recursion for the value function and the optimal strategy of the partially informed investors observing also discrete-time expert opinions.…”