We consider calculation of capital requirements when the underlying economic scenarios are determined by simulatable risk factors. In the respective nested simulation framework, the goal is to estimate portfolio tail risk, quantified via VaR or TVaR of a given collection of future economic scenarios representing factor levels at the risk horizon. Traditionally, evaluating portfolio losses of an outer scenario is done by computing a conditional expectation via innerlevel Monte Carlo and is computationally expensive. We introduce several inter-related machine learning techniques to speed up this computation, in particular by properly accounting for the simulation noise. Our main workhorse is an advanced Gaussian Process (GP) regression approach which uses nonparametric spatial modeling to efficiently learn the relationship between the stochastic factors defining scenarios and corresponding portfolio value. Leveraging this emulator, we develop sequential algorithms that adaptively allocate inner simulation budgets to target the quantile region. The GP framework also yields better uncertainty quantification for the resulting VaR / TVaR estimators that reduces bias and variance compared to existing methods. We illustrate the proposed strategies with two case-studies in two and six dimensions.
We develop a Gaussian process ("GP") framework for modeling mortality rates and mortality improvement factors. GP regression is a nonparametric, data-driven approach for determining the spatial dependence in mortality rates and jointly smoothing raw rates across dimensions, such as calendar year and age. The GP model quantifies uncertainty associated with smoothed historical experience and generates full stochastic trajectories for out-of-sample forecasts. Our framework is well suited for updating projections when newly available data arrives, and for dealing with "edge" issues where credibility is lower. We present a detailed analysis of Gaussian process model performance for US mortality experience based on the CDC (Center for Disease Control) datasets. We investigate the interaction between mean and residual modeling, Bayesian and non-Bayesian GP methodologies, accuracy of in-sample and out-of-sample forecasting, and stability of model parameters. We also document the general decline, along with strong age-dependency, in mortality improvement factors over the past few years, contrasting our findings with the Society of Actuaries ("SOA") MP-2014 and -2015 models that do not fully reflect these recent trends. * Ludkovski is with the
This paper was prepared under Motu's Shaping New Zealand's Low-Emission Future programme, with funding support from the Ministry for Primary Industries and the Aotearoa Foundation. It was informed by the Motu Researcher Workshop on Land Use and Climate Change held in Wellington on 30 April 2018, and we gratefully acknowledge the contributions by presenters and other participants in that process. We also wish to acknowledge Susan Walker from Manaaki Whenua-Landcare Research, who reviewed parts of this paper. Disclaimer Contributions to the researcher workshop and this report were made in individuals' personal capacity and their inclusion in this paper does not imply any recommendation, consensus or endorsement by all participants, their affiliated organisations or the programme funders. While every effort has been made to ensure the information in this publication is accurate, the Ministry for Primary Industries does not accept any responsibility or liability for error of fact, omission, interpretation or opinion that may be present, nor for the consequences of any decisions based on this information.
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