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This paper introduces a general continuous-time mathematical framework for solution of dynamic mean-variance control problems. We obtain theoretical results for two classes of functionals: the first one depends on the whole trajectory of the controlled process and the second one is based on its terminal-time value. These results enable the development of numerical methods for mean-variance problems for a pre-determined risk-aversion coefficient. We apply them to study optimal trading strategies pursued by fund managers in response to various types of compensation schemes. In particular, we examine the effects of continuous monitoring and scheme's symmetry on trading behaviour and fund performance.

Abstract-The availability of complex temporal datasets in social, health and consumer contexts has driven the development of pattern mining techniques that enable the use of classical machine learning tools for model building. In this work we introduce a robust temporal pattern mining framework for finding predictive patterns in complex timestamped multivariate and noisy data. We design an algorithm RobustSPAM that enables mining of temporal patterns from data with noisy timestamps. We apply our algorithm to social care data from a local government body and investigate how the efficiency and accuracy of the method depends on the level of noise. We further explore the trade-off between the loss of predictivity due to perturbation of timestamps and the risk of person re-identification.

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Survival analysis with cohort study data has been traditionally performed using Cox proportional hazards models. Random survival forests (RSFs), a machine learning method, now present an alternative method. Using the UK Women’s Cohort Study (n = 34,493) we evaluate two methods: a Cox model and an RSF, to investigate the association between Body Mass Index and time to breast cancer incidence. Robustness of the models were assessed by cross validation and bootstraping. Histograms of bootstrap coefficients are reported. C-Indices and Integrated Brier Scores are reported for all models. In post-menopausal women, the Cox model Hazard Ratios (HR) for Overweight (OW) and Obese (O) were 1.25 (1.04, 1.51) and 1.28 (0.98, 1.68) respectively and the RSF Odds Ratios (OR) with partial dependence on menopause for OW and O were 1.34 (1.31, 1.70) and 1.45 (1.42, 1.48). HR are non-significant results. Only the RSF appears confident about the effect of weight status on time to event. Bootstrapping demonstrated Cox model coefficients can vary significantly, weakening interpretation potential. An RSF was used to produce partial dependence plots (PDPs) showing OW and O weight status increase the probability of breast cancer incidence in post-menopausal women. All models have relatively low C-Index and high Integrated Brier Score. The RSF overfits the data. In our study, RSF can identify complex non-proportional hazard type patterns in the data, and allow more complicated relationships to be investigated using PDPs, but it overfits limiting extrapolation of results to new instances. Moreover, it is less easily interpreted than Cox models. The value of survival analysis remains paramount and therefore machine learning techniques like RSF should be considered as another method for analysis.