Добірка наукової літератури з теми "Optimal policyholder"

AbstractThe majority of optimal Bonus-Malus Systems (BMS) presented up to now in the actuarial literature assign to each policyholder a premium based on the number of his accidents. In this way a policyholder who had an accident with a small size of loss is penalized unfairly in the same way with a policyholder who had an accident with a big size of loss. Motivated by this, we develop in this paper, the design of optimal BMS with both a frequency and a severity component. The optimal BMS designed are based both on the number of accidents of each policyholder and on the size of loss (severity) for each accident incurred. Optimality is obtained by minimizing the insurer's risk. Furthermore we incorporate in the above design of optimal BMS the important a priori information we have for each policyholder. Thus we propose a generalised BMS that takes into consideration simultaneously the individual's characteristics, the number of his accidents and the exact level of severity for each accident.

Purpose The purpose of this paper is to show how an insurance company can maximize the policyholder’s utility by setting the level of the interest rate guarantee in line with his preferences. Design/methodology/approach The authors develop a general model of life insurance, taking stochastic interest rates, early default and regular premium payments into account. Furthermore, the authors assume that equity holders must receive risk-adequate returns on their initial equity contribution and that the insurance company has to maintain a solvency restriction. Findings The findings show that the optimal level for the interest rate guarantee is in general far below the maximum value typically set by the supervisory authorities and insurance companies. Originality/value The authors conclude that the approach of deviating from the maximum interest rate guarantee level given by the regulatory requirements can create additional value for the rational policyholder. In contrast to Schmeiser and Wagner (2014), the second finding shows that the interest rate guarantee embedded in a life insurance product becomes less attractive compared to a pure investment in the underlying asset portfolio to the policyholder when the guarantee level is lowered too far or the contract duration is short. They also refute Schmeiser and Wagner (2014) by showing that the equity capital required by the insurance company increases with the level of the guarantee, even if the insurer is flexible with respect to its asset allocation. The last finding is that a policyholder with higher risk aversion does not generally prefer a higher guarantee level.

System bonus malus is one of the systems offered by an insurance company where the risk premium calculation is based on the claim history of each policyholder. In study will be discussed premium calculation in system, bonus malus where the frequency of claims has a negative binomial distribution and the size of claims is Weibull distribution on motor vehicle insurance data in Indonesia. This method will producesystem an bonus malus optimal by finding the posterior distribution using Bayes analysis. As the application material used secondary data from the recording results obtained from the general insurance company PT. XYZ in 2014, data contains data on the frequency of claims and the amount ofclaims partial loss of policyholders forinsurance products for comprehensivemotor vehicle insurance category 8 regions 3.The results of the implementation show that the premiums with the system are bonus malus optimalconsidered fair enough because the premiums paid by policyholders insurance that extends the policy in the following year is proportional to the risk it faces, where the premium to be paid by each policyholder is based on past claims history. Keywords: system bonus malus, negative binomial distribution, Weibull distribution, comprehensive, partial loss.

Guaranteed Minimum Income benefit are variable annuities contract, which offer the policyholder the possibility to con- vert the guarantee level into an annuities income for life. This paper focuses on the optimal customer behavior assuming the maximization of the discounted expected future cash flows over the full life of the contract duration. Using convenient scaling properties of the contract value enables to reduce the complexity (dimension) of the problem and to characterize the policyholder’s decision as a function of the contract moneyness across four main choices: zero withdrawals, guaranteed withdrawals, lapse and the income period election. Sensitivities to key drivers such as the market volatility, the interest rate and the roll-up rate illustrate how crucial are not only the environment, but also the product design features, in order to ensure a fair and robust pricing for both customer and life insurer. In particular, the authors find that most empirical contracts are usually underpriced compared to mean optimal behavior pricing, which empirically translated into multiple updates of behavior assumptions and re-reserving by life insurers in the recent years.

AbstractFor insurance companies in Europe, the introduction of Solvency II leads to a tightening of rules for solvency capital provision. In life insurance, this especially affects retirement products that contain a significant portion of longevity risk (e.g., conventional annuities). Insurance companies might react by price increases for those products, and, at the same time, might think of alternatives that shift longevity risk (at least partially) to policyholders. In the extreme case, this leads to so-called tontine products where the insurance company’s role is merely administrative and longevity risk is shared within a pool of policyholders. From the policyholder’s viewpoint, such products are, however, not desirable as they lead to a high uncertainty of retirement income at old ages. In this article, we alternatively suggest a so-called tonuity that combines the appealing features of tontine and conventional annuity. Until some fixed age (the switching time), a tonuity’s payoff is tontine-like, afterwards the policyholder receives a secure payment of a (deferred) annuity. A tonuity is attractive for both the retiree (who benefits from a secure income at old ages) and the insurance company (whose capital requirements are reduced compared to conventional annuities). The tonuity is a possibility to offer tailor-made retirement products: using risk capital charges linked to Solvency II, we show that retirees with very low or very high risk aversion prefer a tontine or conventional annuity, respectively. Retirees with medium risk aversion, however, prefer a tonuity. In a utility-based framework, we therefore determine the optimal tonuity characterized by the critical switching time that maximizes the policyholder’s lifetime utility.

AbstractIn a typical equity-linked life insurance contract, the insurance company is entitled to a share of return surpluses as compensation for the return guarantee granted to the policyholders. The set of possible contract terms might, however, be restricted by a regulatory default constraint — a fact that can force the two parties to initiate sub-optimal insurance contracts. We show that this effect can be mitigated if regulatory policy is more flexible. We suggest that the regulator implement a traffic light system where companies are forced to reduce the riskiness of their asset allocation in distress. In a utility-based framework, we show that the introduction of such a system can increase the benefits of the policyholder without deteriorating the benefits of the insurance company. At the same time, default probabilities (and thus solvency capital requirements) can be reduced.

The extant literature on the Guaranteed Lifetime Withdrawal Benefits (GLWB) financial risk is abundant, however, few articles investigate the option offered to the policyholder with respect to the initiation of the contract and examine this impact on the profitability of the product for the insurer. We extend the analysis carried out by Huang et al. (IME, 2014) on the optimal initiation of the product with GLWB. First, we add an additional dimension in the analysis to account for the insurer losses as a function of the age for disbursement chosen by the policyholder. Then, we develop a novel analytical framework to determine by numerical methods the extent to which an insurer, expecting his client to choose when to receive benefits to maximize the value of his variable annuity contract, should change its actuarially fair fee structure. We show that the fair premium is a function of the insured policyholder age when he bought the contract. This result runs counter to the current fee structure and practice in the Canadian insurance industry with insurers charging a uniform level of fees regardless of the policyholder biological age when the contract is issued.

Purpose This paper aims to theoretically examine the effects of regulatory policyholder protection on spread behavior and default probability of a life insurance company. Design/methodology/approach The authors construct a contingent claim model for the valuation of the equity of a life insurance company. Then, they extend it to model default risk measures associated with a more appropriate behavioral mode of strategic invested asset rate-setting under regulation. Findings The findings established that the optimal insurer interest margin is explicitly modeled by a spread between the loan rate and the required guaranteed rate of the company. The effect of the guaranteed rate on the insurer interest margin is positive when the barrier is low, whereas it is negative when the barrier is high. As the barrier increases, the positive effect of the guaranteed rate on the default risk is increased, the negative effect of the participation on the insurer interest margin is decreased and the positive effect of the participation on the default risk is decreased. Practical implications Several results derived that should be of interest to investors, analysts, supervising agencies and policymakers. For example, policyholders protected by increasing the guaranteed rate may create a higher risk for the life insurance company to meet its obligations. Originality/value The authors’ approach is a significant departure from the existing literature; they differentiate among path-dependent, barrier options and suggest that the life insurance company’s defaults are more commonly triggered by regulatory responses than debt default.

Variable Annuities with embedded guarantees are very popular in the US market. There exists a great variety of products with both, guaranteed minimum death benefits (GMDB) and guaranteed minimum living benefits (GMLB). Although several approaches for pricing some of the corresponding guarantees have been proposed in the academic literature, there is no general framework in which the existing variety of such guarantees can be priced consistently. The present paper fills this gap by introducing a model, which permits a consistent and extensive analysis of all types of guarantees currently offered within Variable Annuity contracts. Besides a valuation assuming that the policyholder follows a given strategy with respect to surrender and withdrawals, we are able to price the contract under optimal policyholder behavior. Using both, Monte-Carlo methods and a generalization of a finite mesh discretization approach, we find that some guarantees are overpriced, whereas others, e.g. guaranteed annuities within guaranteed minimum income benefits (GMIB), are offered significantly below their risk-neutral value.

Policyholder exercise behavior presents an important risk factor for life insurance companies. Yet, most approaches presented in the academic literature – building on value maximizing strategies akin to the valuation of American options – do not square well with observed prices and exercise patterns. Following a recent strand of literature, in order to gain insights on what drives policyholder behavior, I first develop a life-cycle model for variable annuities (VA) with withdrawal guarantees. However, I explicitly allow for outside savings and investments, which considerably affects the results. Specifically, I find that withdrawal patterns after all are primarily motivated by value maximization – but with the important asterisk that the value maximization should be taken out from the policyholders’ perspective accounting for individual tax benefits. To this effect, I develop a risk-neutral valuation methodology that takes these different tax structures into consideration, and apply it to our example contract as well as a representative empirical VA. The results are in line with corresponding outcomes from the life cycle model, and I find that the withdrawal guarantee fee from the empirical product roughly accords with its marginal price to the insurer. I further consider the implications of policyholder behavior on product design. In particular – due to differential tax treatments and contrary to option pricing theory – the marginal value of such guarantees can become negative, even when the holder is a value maximizer. For instance, as I illustrate with both a simple two-period model and an empirical VA, a common death benefit guarantee may indeed yield a negative marginal value to the insurer.

Cette thèse traite plusieurs aspects des risques financiers liés aux contrats d’assurance vie. Elle étudie trois sujets distincts et est composée en six chapitres qui peuvent être lus indépendamment. Le comportement de l’assuré est un risque majeur pour les assureurs dans le cadre de produits d’assurance vie comme les annuités variables. Ainsi, nous nous penchons dans les premiers chapitres sur le comportement optimal pour deux classes de produits commercialisés. Nous traitons le cas du rachat total pour les « guaranteed minimum account benefits » (GMAB), et le retrait optimal dans le cadre des « guaranteed minimum income benefit » (GMIB). Le troisième chapitre est dédié au management et à la couverture d’une classe de produits à unité de compte également commercialisés par les assurances.Le second sujet consiste en un chapitre et traite l’exécution optimal d’un large portefeuille d’options. En effet, les produits d’assurance vie sont partiellement couverts statiquement par la détention d’options vanilles. Nous considérons le cas où la taille des trades affecte le prix des options et cherchons à définir la stratégie optimale permettant de minimiser le coût de l’acquisition de ce portefeuille de couverture, en prenant en compte l’impact de marché.Enfin, le dernier thème de la thèse étudie le processus de volatilité. A cet effet, nous utilisons deux types d’estimateurs. En l’absence de données haute fréquence, les estimateurs dit de « range » permettent de revérifier que la volatilité est rugueuse. Ensuite, en utilisant les prix d’options, la volatilité implicite et une version raffinée de cette dernière permettent encore une fois d’aboutir à la même conclusion
This thesis tackles several aspects of financial risks encountered in the life insurance industry and particularly in a class of the products insurers offer; namely variable annuities and unit-linked products. It consists of three distinct topics and is split into six chapter that can be read independently.In variable annuities (VAs), policyholders’ behavior is a major risk for the insurer that affects life insurance industry in almost every aspect. The first two chapters of this first part deal with policyholders’ optimal policyholder for two VAs products. We address the rational lapse behavior in the guaranteed minimum account benefit (GMAB), and optimal withdrawals in the guaranteed minimum income benefit (GMIB). The third chapter is dedicated to a class of unit-linked products from a managing and hedging point of view. The second topic consists of one chapter and addresses the optimal execution of a large book of options. Typically, life insurance products are partially hedged using vanilla options. We consider the case where trades are affected by the traded quantity, and seek to find an optimal strategy that minimizes the expected cost and the mean-variance criterion.Finally, in the last topic we study the volatility process using two different proxies. First, range based estimators that rely on the asset price range data allow us to double-check that volatility is a rough process in the sense that it has a scaling parameter H less than 1/2. Then, using short time-to-maturity implied volatility, and a refined version of it, allows us to confirm that the rough aspect of volatility is universal along different proxies