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Solving High-Dimensional Dynamic Portfolio Choice Models with Hierarchical B-Splines on Sparse Grids
(2021)
Discrete time dynamic programming to solve dynamic portfolio choice models has three immanent issues: firstly, the curse of dimensionality prohibits more than a handful of continuous states. Secondly, in higher dimensions, even regular sparse grid discretizations need too many grid points for sufficiently accurate approximations of the value function. Thirdly, the models usually require continuous control variables, and hence gradient-based optimization with smooth approximations of the value function is necessary to obtain accurate solutions to the optimization problem. For the first time, we enable accurate and fast numerical solutions with gradient-based optimization while still allowing for spatial adaptivity using hierarchical B-splines on sparse grids. When compared to the standard linear bases on sparse grids or finite difference approximations of the gradient, our approach saves an order of magnitude in total computational complexity for a representative dynamic portfolio choice model with varying state space dimensionality, stochastic sample space, and choice variables.
Background and aims: Individualization of treatment with peginterferon alfa and ribavirin in patients with chronic hepatitis C showed benefit in controlled trials and was implemented in treatment guidelines to increase response rates and to reduce side effects and costs. However, it is unknown whether individualization was adopted in routine daily practice and whether it translated into improved outcomes.
Methods: From a large noninterventional cohort study, clinical and virologic response data of 10,262 HCV patients who received peginterferon alfa-2a and ribavirin between 2003-2007 and 2008-2011 were analyzed. To account for treatment individualization, a matched-pair analysis (2,997 matched pairs) was performed. Variation in treatment duration and dosing of ribavirin were analyzed as indicators for individualization.
Results: Sustained virological response (SVR) rates were similar between 2003-2007 and 2008-2011 (62.0% vs. 63.7%). Patients with comorbidities were more abundant in the later period, (44.3% vs. 57.1%). The subsequent matched-pair analysis demonstrated higher SVR rates in the 2008-2011 period (64.3%) than in the 2003-2007 period (61.2%, p=0.008). More patients received abbreviated or extended treatment regimens in the later than the earlier period as an indicator of treatment individualization. To the same end, ribavirin doses were higher in the later period (12.6 versus 11.6 mg/kg/day). Factors independently associated with SVR included HCV genotype, low baseline viral load, younger age, route of infection, absence of concomitant diseases, lower APRI score, normal gamma-GT, higher ribavirin doses, no substitution for drug abuse, treatment duration, and treatment in the 2008-2011 period.
Conclusions: Treatment individualization with peginterferon alfa and ribavirin was implemented in daily routine between 2003-2007 and 2008-2011, SVR rates improved in the same period. These findings may be most relevant in resource-limited settings.
Correction to: Computational Economics https://doi.org/10.1007/s10614-020-10061-x
The original publication has been updated. In the original publication of this article, under the Introduction heading section, the corrections to the second paragraph’s inline equation were not incorporated. The author’s additional corrections have also been incorporated. The publisher apologizes for the error made during production.