High‐order split‐step theta methods for non‐autonomous stochastic differential equations with non‐globally Lipschitz continuous coefficients

In this paper, we first propose the so‐called improved split‐step theta methods for non‐autonomous stochastic differential equations driven by non‐commutative noise. Then, we prove that the improved split‐step theta method is convergent with strong order of one for stochastic differential equations with the drift coefficient satisfying a superlinearly growing condition and a one‐sided Lipschitz continuous condition. Finally, the obtained results are verified by numerical experiments. Copyright © 2016 John Wiley & Sons, Ltd.     

Infinite horizon optimal policy for an inventory system with two types of product sharing common hardware platforms

We consider a periodic review inventory system and present its optimal policy in the infinite horizon setting. The optimal inventory policy that maximizes the infinite horizon expected discounted profit for the model is analytically obtained by relating to the finite horizon setting using results from variational analysis. Results are provided that elucidate the operations of the inventory system in the long run.     

Optimal insurance design in the presence of exclusion clauses

The present work studies the design of an optimal insurance policy from the perspective of an insured, where the insurable loss is mutually exclusive from another loss that is denied in the insurance coverage. To reduce ex post moral hazard, we assume that both the insured and the insurer would pay more for a larger realization of the insurable loss. When the insurance premium principle preserves the convex order, we show that any admissible insurance contract is suboptimal to a two-layer insurance policy under the criterion of minimizing the insured’s total risk exposure quantified by value at risk, tail value at risk or an expectile. The form of optimal insurance can be further simplified to be one-layer by imposing an additional weak condition on the premium principle. Finally, we use Wang’s premium principle and the expected value premium principle to illustrate the applicability of our results, and find that optimal insurance solutions are affected not only by the size of the excluded loss but also by the risk measure chosen to quantify the insured’s risk exposure.     

Asset liability management for open pension schemes using multistage stochastic programming under Solvency-II-based regulatory constraints

Open private pension schemes are subject to risk-based regulation. In this context, asset and liability management (ALM) frameworks for pension plan operators are increasingly based on multistage stochastic programming (MSP). The significant advances in MSP modeling notwithstanding, previous works ignore risk-based regulatory constraints such as those in the Solvency II Directive. In this work, we propose an ALM model for open pension schemes based on an MSP model with a thorough representation of a risk-based regulation. Our proposal aims to define a dynamic optimal asset allocation including a detailed depiction of bond coupon payments, based on insolvency risk measures over a planning horizon. We present a realistic case study based on the Brazilian market, where the regulator imposes Solvency-II-compatible constraints on credit, underwriting, and operational risks. We develop a computationally tractable MSP model with explicit regulatory constraints, which induce risk aversion for even risk-neutral open pension plan operators.     

A Dirichlet form approach to MCMC optimal scaling

This paper shows how the theory of Dirichlet forms can be used to deliver proofs of optimal scaling results for Markov chain Monte Carlo algorithms (specifically, Metropolis–Hastings random walk samplers) under regularity conditions which are substantially weaker than those required by the original approach (based on the use of infinitesimal generators). The Dirichlet form methods have the added advantage of providing an explicit construction of the underlying infinite-dimensional context. In particular, this enables us directly to establish weak convergence to the relevant infinite-dimensional distributions.     

Singular mean-field control games

This article studies singular mean field control problems and singular mean field two-players stochastic differential games. Both sufficient and necessary conditions for the optimal controls and for the Nash equilibrium are obtained. Under some assumptions the optimality conditions for singular mean-field control are reduced to a reflected Skorohod problem, whose solution is proved to exist uniquely. Motivations are given as optimal harvesting of stochastic mean-field systems, optimal irreversible investments under uncertainty and mean-field singular investment games. In particular, a simple singular mean-field investment game is studied, where the Nash equilibrium exists but is not unique.     

广义正交表和正交表的裂区试验设计法的比较

裂区试验设计方法是在正交表的基础上进行的.根据试验设计的数据分析结论要求具有再现性这一原理,将证明这种裂区试验设计法要有条件的使用才是合理的.由于广义正交表是保证设计表具有再现性的基本设计表,根据广义正交表来研究这种裂区试验设计方法的合理性.研究结果显示在裂区试验设计法对应的设计表是广义正交表,并且相应的数据分析方法采用广义正交表的数据分析方法时,才能保证其数据分析结论具有客观一致性和可重复再现性.     

Optimal harvesting for a stochastic logistic model with S-type distributed time delay

In this paper, the optimization problem of harvesting for a stochastic logistic model with S-type distributed time delay (which contains both discrete time delay and continuously distributed time delay) is studied by using ergodic method.     

Grouped Functional Time Series Forecasting: An Application to Age-Specific Mortality Rates

Age-specific mortality rates are often disaggregated by different attributes, such as sex, state, and ethnicity. Forecasting age-specific mortality rates at the national and sub-national levels plays an important role in developing social policy. However, independent forecasts at the sub-national levels may not add up to the forecasts at the national level. To address this issue, we consider reconciling forecasts of age-specific mortality rates, extending the methods of Hyndman et al. in 2011 Hyndman, R. J., Ahmed, R. A., Athanasopoulos, G., and Shang, H. L. (2011), “Optimal Combination Forecasts for Hierarchical Time Series,” Computational Statistics and Data Analysis, 55, 2579–2589.[Crossref], [Web of Science ®] , [Google Scholar] to functional time series, where age is considered as a continuum. The grouped functional time series methods are used to produce point forecasts of mortality rates that are aggregated appropriately across different disaggregation factors. For evaluating forecast uncertainty, we propose a bootstrap method for reconciling interval forecasts. Using the regional age-specific mortality rates in Japan, obtained from the Japanese Mortality Database, we investigate the one- to ten-step-ahead point and interval forecast accuracies between the independent and grouped functional time series forecasting methods. The proposed methods are shown to be useful for reconciling forecasts of age-specific mortality rates at the national and sub-national levels. They also enjoy improved forecast accuracy averaged over different disaggregation factors. Supplementary materials for the article are available online.     

A note on two fixed point problems

We extend the applicability of the Exterior Ellipsoid Algorithm for approximating n-dimensional fixed points of directionally nonexpanding functions. Such functions model many practical problems that cannot be formulated in the smaller class of globally nonexpanding functions. The upper bound 2n²ln(2/) on the number of function evaluations for finding -residual approximations to the fixed points remains the same for the larger class. We also present a modified version of a hybrid bisection-secant method for efficient approximation of univariate fixed point problems in combustion chemistry.