Optimal mean–variance efficiency of a family with life insurance under inflation risk

We study an optimization problem of a family under mean–variance efficiency. The market consists of cash, a zero-coupon bond, an inflation-indexed zero-coupon bond, a stock, life insurance and income-replacement insurance. The instantaneous interest rate is modeled as the Cox–Ingersoll–Ross (CIR) model, and we use a generalized Black–Scholes model to characterize the stock and labor income. We also take into account the inflation risk and consider our problem in the real market. The goal of the family is to maximize the mean of the surplus wealth at the retirement or death of the breadwinner and minimize its variance by finding a portfolio selection. The efficient frontier and optimal strategies are derived through the dynamic programming method and the technique of solving associated nonlinear HJB equations. We also present a numerical illustration to explore the impact of economical parameters on the efficient frontier.     

A bonus—malus system in automobile insurance

The Storebrand Insurance Company has introduced a new bonus—malus system for automobile insurance (passenger cars) into the Norwegian market. The new system differs from traditional bonus—malus systems mainly due to the fact that bonus reduction after a claim is expressed by a fixed monetary amount. This paper describes the practical implementation of the bonus—malus system.     

Optimal preventive maintenance scheduling of thermal generating units in power systems —A survey of problem formulations and solution methods

Preventive maintenance scheduling of thermal generating units occupies a significant place in power system operation and expansion planning; at the same time it is a challenging optimization problem. The purpose of this paper is to analyse essential features of the maintenance scheduling problem, including imposed constraints and various objectives, as well as to present the results of the research work done in this field using operational research methods. Papers published during last fifteen years are discussed, with special regard for the applied optimization techniques.     

Dynamic hybrid products in life insurance: Assessing the policyholders’ viewpoint

Dynamic hybrid life insurance products are intended to meet new consumer needs regarding stability in terms of guarantees as well as sufficient upside potential. In contrast to traditional participating or classical unit-linked life insurance products, the guarantee offered to the policyholders is achieved by a periodical rebalancing process between three funds: the policy reserves (i.e. the premium reserve stock, thus causing interaction effects with traditional participating life insurance contracts), a guarantee fund, and an equity fund. In this paper, we consider an insurer offering both, dynamic hybrid and traditional participating life insurance contracts and focus on the policyholders’ perspective. The results show that higher guarantees do not necessarily imply a higher willingness-to-pay, but that in case of dynamic hybrid contracts, a minimum guarantee level should be offered in order to ensure that the willingness-to-pay exceeds the minimum premium the insurer has to charge when selling the contract. In addition, strong interaction effects can be found between the two products, which particularly impact the willingness-to-pay of the dynamic hybrids.     

An analysis of transaction costs in participating life insurance under mean–variance preferences

Transaction costs with respect to distribution and administration play a crucial role for the performance of participating life insurance products. The aim of this paper is to investigate the impact of such initial and annual transaction costs on policyholder mean–variance preferences depending on the contract features, comparing a point-to-point guarantee, a cliquet-style guarantee, and a money-back guarantee with annual surplus component. We extend previous work by deriving analytical solutions for the maximum allowed initial transaction costs as well as the risk aversion parameter that ensure a given customer preference level for different contract types. We further conduct simulation analyses to identify key factors in regard to transaction costs. One main finding is that in the present setting, insurers can indeed charge higher costs for more complex products with cliquet-style features, and that the difference in costs between the various product types increases considerably in a low interest-rate environment. However, these results are heavily impacted and even reversed depending on the risk–return asset characteristics, as insurers with a riskier asset management strategy may no longer be able to charge higher transaction costs for complex products with a strong annual cliquet-style surplus participation component without reducing their attractiveness to customers.     

Lapse risk in life insurance: Correlation and contagion effects among policyholders’ behaviors

The present paper proposes a new methodology to model the lapse risk in life insurance by integrating the dynamic aspects of policyholders’ behaviors and the dependency of the lapse intensity on macroeconomic conditions. Our approach, suitable to stable economic regimes as well as stress scenarios, introduces a mathematical framework where the lapse intensity follows a dynamic contagion process, see Dassios and Zhao (2011). This allows to capture both contagion and correlation potentially arising among insureds’ behaviors. In this framework, an external market driven jump component drives the lapse intensity process depending on the interest rate trajectory: when the spread between the market interest rates and the contractual crediting rate crosses a given threshold, the insurer is likely to experience more surrenders. A log-normal dynamic for the forward rates is introduced to build trajectories of an observable market variable and mimic the effect of a macroeconomic triggering event based on interest rates on the lapse intensity. Contrary to previous works, our shot-noise intensity is not constant and the resulting intensity process is not Markovian. Closed-form expressions and analytic sensitivities for the moments of the lapse intensity are provided, showing how lapses can be affected by massive copycat behaviors. Further analyses are then conducted to illustrate how the mean risk varies depending on the model’s parameters, while a simulation study compares our results with those obtained using standard practices. The numerical outputs highlight a potential misestimation of the expected number of lapses under extreme scenarios when using classical stress testing methodologies.     

Optimal decay rate of solutions for Cahn–Hilliard equation with inertial term in multi-dimensions

The Cauchy problem of the Cahn–Hilliard equation with inertial term is considered. Based on Green?s function method together with energy estimates, we get the global-in-time existence and optimal decay rate of solutions. Furthermore, the viscous case is investigated in the last section.     

A correction term for Gauss–Gegenbauer quadrature

By means of Chebyshev polynomials of the first kind a correction term for Gauss–Gegenbauer quadrature is derived.     

Optimal valuation of American callable credit default swaps under drawdown of Lévy insurance risk process

This paper discusses the valuation of credit default swaps, where default is announced when the reference asset price has gone below certain level from the last record maximum, also known as the high-water mark or drawdown. We assume that the protection buyer pays premium at a fixed rate when the asset price is above a pre-specified level and continuously pays whenever the price increases. This payment scheme is in favour of the buyer as she only pays the premium when the market is in good condition for the protection against financial downturn. Under this framework, we look at an embedded option which gives the issuer an opportunity to call back the contract to a new one with reduced premium payment rate and slightly lower default coverage subject to paying a certain cost. We assume that the buyer is risk neutral investor trying to maximize the expected monetary value of the option over a class of stopping time. We discuss optimal solution to the stopping problem when the source of uncertainty of the asset price is modelled by Lévy process with only downward jumps. Using recent development in excursion theory of Lévy process, the results are given explicitly in terms of scale function of the Lévy process. Furthermore, the value function of the stopping problem is shown to satisfy continuous and smooth pasting conditions regardless of regularity of the sample paths of the Lévy process. Optimality and uniqueness of the solution are established using martingale approach for drawdown process and convexity of the scale function under Esscher transform of measure. Some numerical examples are discussed to illustrate the main results.     

A parametric solution for simple stress—strength model of failure with an application

Estimation of P(R ⩽ S) is considered for the simple stress—strength model of failure. Using the Pareto and Power distributions together with their combined form a useful parametric solution is obtained and is illustrated numerically. It is shown that these models are also applicable when only the tails of distributions for R and S are considered. An application to the failure study concerning the fractures is also included     

A dependent frequency–severity approach to modeling longitudinal insurance claims

In nonlife insurance, frequency and severity are two essential building blocks in the actuarial modeling of insurance claims. In this paper, we propose a dependent modeling framework to jointly examine the two components in a longitudinal context where the quantity of interest is the predictive distribution. The proposed model accommodates the temporal correlation in both the frequency and the severity, as well as the association between the frequency and severity using a novel copula regression. The resulting predictive claims distribution allows to incorporate the claim history on both the frequency and severity into ratemaking and other prediction applications. In this application, we examine the insurance claim frequencies and severities for specific peril types from a government property insurance portfolio, namely lightning and vehicle claims, which tend to be frequent in terms of their count. We discover that the frequencies and severities of these frequent peril types tend to have a high serial correlation over time. Using dependence modeling in a longitudinal setting, we demonstrate how the prediction of these frequent claims can be improved.     

Analyzing legal regulations in the Norwegian life insurance business using a multistage asset–liability management model

The legal regulations for the life insurance business in Norway have recently been, and still are, under revision. The government's intention is to secure the interests of the customers in life insurance companies. However, there has been debate as to whether the regulations really are in the customers' best interest. We apply an asset–liability management (ALM) model to analyze the implications of the regulations. The model is multistage, stochastic and integrates assets and liabilities. We employ a four stage model to analyze the legal regulations, and conclude that the current legal framework is not in the insurance holders' best interests.     

Entropy solution for a nonlinear elliptic problem with lower order term in Musielak–Orlicz spaces

In this paper, we shall be concerned with the existence result of the following problem,

$$\begin{aligned} \left\{ \begin{array}{l} -\text {div}\left( a(x,u,\nabla u)\right) -\text {div}(\Phi (x,u))= f \ \ \mathrm{in}\ \Omega ,\\ u=0 \text { on } \partial \Omega , \end{array} \right. \end{aligned}$$

(0.1)

with the second term f belongs to \(L^1(\Omega )\). The growth and the coercivity conditions on the monotone vector field a are prescribed by a generalized N-function M. We assume any restriction on M, therefore we work with Musielak–Orlicz spaces which are not necessarily reflexive. The lower order term \(\Phi \) is a Carathéodory function satisfying only a growth condition.

     

Locally risk-minimizing hedging strategies for unit-linked life insurance contracts under a regime switching L��vy model

This paper extends the model and analysis in that of Vandaele and Vanmaele [Insurance: Mathematics and Economics, 2008, 42: 1128–1137]. We assume that parameters of the Lévy process which models the dynamic of risky asset in the financial market depend on a finite state Markov chain. The state of the Markov chain can be interpreted as the state of the economy. Under the regime switching Lévy model, we obtain the locally risk-minimizing hedging strategies for some unit-linked life insurance products, including both the pure endowment policy and the term insurance contract.     

Optimal segmentation of projects — Schedule and cost considerations

In certain types of projects, the same sequence of activities is performed throughout the various physical parts of the project (e.g., road construction). By dividing the project into segments and working in parallel, the duration of the project can be reduced, with a resulting increase in direct costs. In this paper we consider the problem of finding the optimal number of segments that minimizes total project cost, for linear cost and duration functions. We begin by formulating and solving a mathematical programming model for homogeneous projects, and, by using the concept of work contents, we extend the solution to non-homogeneous projects.     

A Characterization of the Optimal p-sum Labellingsof Unit Interval Graphs

1.IntroductionGraphsconsideredinthispaperarefiniteandsimple.FOragraphG,V(G)andE(G)denoteitssetofvenicesandedges,respectively.AbijectionwillbecalledalabellingofG.Letpbeapositiverealnumber.ForagivenlabellingTofagraphG,definethegndiscrepencya.(G,ac)ofTasTheobjectiveoftheminimum-p--sumproblemistofindalabelling7ofagraphGsuchthatac(G,T)isassmallaspossible.ThelabellingTminimizinga.(G,7)iscalledanoptimalHsumlabellingofG.Theminimumvalueiscalledtheminimum-psumofG.ItisshowninI31thattheminimum-…     

A measurable-group-theoretic solution to von Neumann’s problem

We give a positive answer, in the measurable-group-theory context, to von Neumann’s problem of knowing whether a non-amenable countable discrete group contains a non-cyclic free subgroup. We also get an embedding result of the free-group von Neumann factor into restricted wreath product factors. D. Gaboriau’s research was supported by CNRS. R. Lyons’ research was supported partially by NSF grant DMS-0705518 and Microsoft Research.     

A Borel solution to the Horn–Tarski problem

We describe a Borel poset satisfying the σ-finite chain condition but failing to satisfy the σ-bounded chain condition.     

Overlaying Classifiers: A Practical Approach to Optimal Scoring

The Receiver Operating Characteristic (ROC) curve is one of the most widely used visual tools to evaluate performance of scoring functions regarding their capacities to discriminate between two populations. It is the goal of this paper to propose a statistical learning method for constructing a scoring function with nearly optimal ROC curve. In this bipartite setup, the target is known to be the regression function up to an increasing transform, and solving the optimization problem boils down to recovering the collection of level sets of the latter, which we interpret here as a continuum of imbricated classification problems. We propose a discretization approach, consisting of building a finite sequence of N classifiers by constrained empirical risk minimization and then constructing a piecewise constant scoring function s _N (x) by overlaying the resulting classifiers. Given the functional nature of the ROC criterion, the accuracy of the ranking induced by s _N (x) can be conceived in a variety of ways, depending on the distance chosen for measuring closeness to the optimal curve in the ROC space. By relating the ROC curve of the resulting scoring function to piecewise linear approximates of the optimal ROC curve, we establish the consistency of the method as well as rate bounds to control its generalization ability in sup -norm. Eventually, we also highlight the fact that, as a byproduct, the algorithm proposed provides an accurate estimate of the optimal ROC curve.