This paper discusses the use of modelling techniques for the purpose of risk management within life insurers. The key theme of the paper is that life insurance is long-term business and carries with it long-term risks, yet much of modern actuarial risk management is focussed on short-term modelling approaches. These typically include the use of copula simulation models within a 1-year Value-at-Risk (VaR) framework. The paper discusses the limitations inherent within the techniques currently used in the UK and discusses how the focus of the next generation of actuarial models may be on long-term stochastic projections. The scope of the paper includes a discussion of how existing techniques, together with new approaches, may be used to develop such models and the benefits this can bring. The paper concludes with a practical example of how a long-term stochastic risk model may be implemented.

The light-induced reorientation of the cortical microtubule array in dark-grown Arabidopsis thaliana hypocotyl cells is a striking example of the dynamical plasticity of the microtubule cytoskeleton. A consensus model, based on katanin-mediated severing at microtubule crossovers, has been developed that successfully describes the onset of the observed switch between a transverse and longitudinal array orientation. However, we currently lack an understanding of why the newly populated longitudinal array direction remains stable for longer times and re-equilibration effects would tend to drive the system back to a mixed orientation state. Using both simulations and analytical calculations, we show that the assumption of a small orientation-dependent shift in microtubule dynamics is sufficient to explain the long-term lock-in of the longitudinal array orientation. Furthermore, we show that the natural alternative hypothesis that there is a selective advantage in severing longitudinal microtubules, is neither necessary nor sufficient to achieve cortical array reorientation, but is able to accelerate this process significantly.

India is one of the severely affected countries by the Covid-19 pandemic at present. Within the stochastic framework of the SEQIR model, we studied publicly available data of the Covid-19 patients in India and analysed possible impacts of quarantine and social distancing as controlling strategies for the pandemic. Our stochastic simulation results clearly show that proper quarantine and social distancing should be maintained right from the start of the pandemic and continued until its end for effective control. This calls for a more disciplined social lifestyle in the future. However, only social distancing and quarantine of the exposed population are found not sufficient enough to end the pandemic in India. Therefore, implementation of other stringent policies like complete lockdown as well as increased testing of susceptible populations is necessary. The demographic stochasticity, which is quite visible in the system dynamics, has a critical role in regulating and controlling the pandemic.

The prevalent presence of a single chiral variant of molecules in live organisms is one of the most distinctive signs of life as a global phenomenon. One of the greatest ambitions of biochemistry and astrobiology is to provide an explanation of this predominance. Several mechanisms were proposed in the past, from the propagation of chirality from a homo-chiral substrate to the amplification of effects associated with electro-weak interactions. Here, a different scenario is proposed: anomalous fluctuations associated with a self-replication scenario can lead to the selective extinction of primordial organisms using one of two enantiomers as an enzyme. These fluctuations arise spontaneously under very general conditions. The idea is based on three key points: (a) the simulation of early biological processes as a ‘board game’; (b) the presence of large fluctuations during an autocatalytic process; (c) the presence of a limited source of chemical energy, inducing a form of competition in a primordial replicator population. In order to demonstrate this mechanism, a computational model is developed, describing the ‘struggle for life’ of two different kinds of primordial replicators on a ‘chessboard’ with periodic boundary conditions; each replicator employs enzymes of different chirality on a non-chiral substrate, thereby with no selective advantage. The replication occurs randomly and with a fixed probability, providing that a sufficient amount of chemical energy is locally available. For the first time, our model includes the local balance of chemical energy in a molecular form on the substrate. The correlation between the chemical energy and the local populations is shown. Results clearly show that strong fluctuations in the number of individuals of each species and subsequent selective extinction events of one of the two species are observed. These studies may contribute to shed light on the most mysterious phase transition that occurred during the biochemical evolution of our planet.

The paper deals with prognosis estimation for industrial systems in a series configuration, modeled by superimposed renewal processes (SRP), when the cause of failures is not available. In the presence of missing information, an SRP is commonly approximated by a Poisson process or a virtual age model. The performance of the approximations was assessed in the ideal configuration where all parameters of the models are known. The current article adopts a practitioner's perspective by assuming that the parameters of the models are unknown and must be estimated. In addition to inference procedures, the assessment of the prognosis indicators, such as the remaining useful life, is discussed. Finally, we investigate a fleet of infrastructure components of the Norwegian railway network operated by Bane NOR.

We propose a novel time discretization for the log-normal SABR model which is a popular stochastic volatility model that is widely used in financial practice. Our time discretization is a variant of the Euler–Maruyama scheme. We study its asymptotic properties in the limit of a large number of time steps under a certain asymptotic regime which includes the case of finite maturity, small vol-of-vol and large initial volatility with fixed product of vol-of-vol and initial volatility. We derive an almost sure limit and a large deviations result for the log-asset price in the limit of a large number of time steps. We derive an exact representation of the implied volatility surface for arbitrary maturity and strike in this regime. Using this representation, we obtain analytical expansions of the implied volatility for small maturity and extreme strikes, which reproduce at leading order known asymptotic results for the continuous time model.

Reliability theory and survival analysis, the residual entropy is known as a measure suitable to describe the dynamic information content in stochastic systems conditional on survival. Aiming to analyze the variability of such information content, in this paper we introduce the variance of the residual lifetimes, “residual varentropy” in short. After a theoretical investigation of some properties of the residual varentropy, we illustrate certain applications related to the proportional hazards model and the first-passage times of an Ornstein–Uhlenbeck jump-diffusion process.

This paper describes the use of a stochastic model of the full regulatory balance sheet of an insurer under the Solvency II regime. The purpose of the model is to enable firms to understand the key risks that threaten the regulatory solvency of the firm and therefore its long-term business objectives.

Stochastic ordering of random variables may be defined by the relative convexity of the tail functions. This has been extended to higher order stochastic orderings, by iteratively reassigning tail-weights. The actual verification of stochastic orderings is not simple, as this depends on inverting distribution functions for which there may be no explicit expression. The iterative definition of distributions, of course, contributes to make that verification even harder. We have a look at the stochastic ordering, introducing a method that allows for explicit usage, applying it to the Gamma and Weibull distributions, giving a complete description of the order of relations within each of these families.

In many scheduling applications, minimizing delays is of high importance. One adverse effect of such delays is that the reward for completion of a job may decay over time. Indeed in healthcare settings, delays in access to care can result in worse outcomes, such as an increase in mortality risk. Motivated by managing hospital operations in disaster scenarios, as well as other applications in perishable inventory control and information services, we consider non-preemptive scheduling of jobs whose internal value decays over time. Because solving for the optimal scheduling policy is computationally intractable, we focus our attention on the performance of three intuitive heuristics: (1) a policy which maximizes the expected immediate reward, (2) a policy which maximizes the expected immediate reward rate, and (3) a policy which prioritizes jobs with imminent deadlines. We provide performance guarantees for all three policies and show that many of these performance bounds are tight. In addition, we provide numerical experiments and simulations to compare how the policies perform in a variety of scenarios. Our theoretical and numerical results allow us to establish rules-of-thumb for applying these heuristics in a variety of situations, including patient scheduling scenarios.

We consider the multi-armed bandit problem under a cost constraint. Successive samples from each population are i.i.d. with unknown distribution and each sample incurs a known population-dependent cost. The objective is to design an adaptive sampling policy to maximize the expected sum of n samples such that the average cost does not exceed a given bound sample-path wise. We establish an asymptotic lower bound for the regret of feasible uniformly fast convergent policies, and construct a class of policies, which achieve the bound. We also provide their explicit form under Normal distributions with unknown means and known variances.

In this paper, we study an M/M/1 queue, where the server continues to work during idle periods and builds up inventory. This inventory is used for new arriving service requirements, but it is completely emptied at random epochs of a non-homogeneous Poisson process, whose rate depends on the current level of the acquired inventory. For several shapes of depletion rates, we derive differential equations for the stationary density of the workload and the inventory level and solve them explicitly. Finally, numerical illustrations are given for some particular examples, and the effects of this depletion mechanism are discussed.

We study the degree profile of random hierarchical lattice networks. At every step, each edge is either serialized (with probability p) or parallelized (with probability 1−p). We establish an asymptotic Gaussian law for the number of nodes of outdegree 1, and show how to extend the derivations to encompass asymptotic limit laws for higher outdegrees. The asymptotic joint distribution of the number of nodes of outdegrees 1 and 2 is shown to be bivariate normal. No phase transition with p is detected in these asymptotic laws.

For the limit laws, we use ideas from the contraction method. The recursive equations which we get involve coefficients and toll terms depending on the recursion variable and thus are not in the standard form of the contraction method. Yet, an adaptation of the contraction method goes through, showing that the method has promise for a wider range of random structures and algorithms.

For the birth–death process on a finite state space with bilateral boundaries, we give a simpler derivation of the hitting time distributions by h-transform and φ-transform. These transforms can then be used to construct a quick derivation of the hitting time distributions of the minimal birth–death process on a denumerable state space with exit/regular boundaries.

In this paper, the first study of stochastic economic modelling with Chinese data is conducted for actuarial use. Univariate models, vector autoregression and two cascade systems (equity-driving cascade system and price-inflation-driving cascade system) are described and compared. We focus on six major economic assumptions for modelling purposes, which are price inflation rate, wage inflation rate, long-term interest rate, short-term interest rate, equity total return and bond total return. Granger causality tests are used to identify the driving force of a cascade system. Robust standard errors are estimated for each model. Diagnostic checking of residuals, goodness-of-fit measures and out-of-sample validations are applied for model selection. By comparing different models for each variable, we find that the equity-driving cascade system is the best structure for actuarial use in China. The forecasts of the variables could be applied as economic inputs to stochastic projection models of insurance portfolios or pension funds for short-term asset and liability cash flow forecasting.

The Geological Survey of the Netherlands aims at building a 3D geological voxel model of the upper 30 m of the subsurface of the Netherlands in order to provide a sound basis for subsurface related questions on, amongst others, groundwater extraction and management, land subsidence studies, aggregate resources and infrastructural issues. The Province of Zeeland (SW Netherlands, covering an area of approximately 70 by 75 km) was chosen as the starting point for this model due to an excellent dataset of 23,000 stratigraphically interpreted borehole descriptions.

The modelling procedure involved a number of steps. The first step is a geological schematisation of the borehole descriptions into units that have uniform sediment characteristics, using lithostratigraphical, lithofacies and lithological criteria. During the second modelling step, 2D bounding surfaces are constructed. These surfaces represent the top and base of the lithostratigraphical units and are used to place each voxel (100 by 100 by 0.5 metres) in the model within the correct lithostratigraphical unit. The lithological units in the borehole descriptions are used to perform a final 3D stochastic interpolation of lithofacies, lithology (clay, sand, peat) and if applicable, sand grain-size class within each lithostratigraphical unit. After this step, a three-dimensional geological model is obtained. The use of stochastic techniques such as Sequential Gaussian Simulation and Sequential Indicator Simulation, allowed us to compute probabilities for lithostratigraphy, lithofacies and lithology for each voxel, providing a measure of model uncertainty.

The procedures described above resulted in the first fully 3D regional-scale lithofacies model of the shallow subsurface in the Netherlands. The model provides important new insights on spatial connectivity of sediment units of, for example, sandy Holocene tidal channel systems. Our results represent a major step forward towards a fully 3D voxel model of the Netherlands.

This article considers the amount of economic capital that defined benefit (DB) pension schemes potentially need to cover the risks they are running. A real open scheme, the Universities Superannuation Scheme, is modelled and used to illustrate our results and, as expected, economic capital requirements are large. We discuss the appropriateness of these results and what they mean for the DB pension scheme industry and their sponsors. The article is particularly pertinent following the recent European Commission Green Paper on the future of European pensions systems, its call for advice on reviewing the Institutions for Occupational Retirement Provision Directive and the introduction of the Basel 2 and Solvency 2 risk-based regulatory regimes for banking and insurance, respectively.

Investment strategy is often static, punctuated by infrequent reviews. For most long-term investors, this practice results in large risks being taken that could otherwise be managed with a more dynamic investment policy. The bulk of this paper is aimed at analysing and describing two multi-period investment strategy problems — in order to derive potential dynamic strategies. Along the way, we show how static investment strategies can fail to deliver an investor's long-term objectives and describe the relationship of our work to other areas of the finance literature. This paper does not cover trading strategies such as Tactical Asset Allocation.

This paper sets out two main approaches to the multi-period problem. The first approach optimises a utility function. The second approach uses partial differential equation (PDE) technology to optimise a target statistic (in this case, TailVaR) subject to return and long-only constraints.