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1.
What if Variable Annuity Policyholders With Guaranteed Lifelong Withdrawal Benefit Were Rational?
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This article examines the lapse risk inherent to the guaranteed lifelong withdrawal benefit option embedded in a variable annuity product valuated from a pure derivatives perspective, that is, as a Bermudian option given to the policyholder. We assume rational behavior and quantify the potential impact of the lapse risk, defined as the difference between no lapse and optimal lapsing. We develop a sensitivity analysis that shows how the value of the product varies with the key parameters, and calculate the fair fee using Monte Carlo simulations. Empirical analyses are performed and numerical results are provided. 相似文献
2.
Abstract One of the acknowledged difficulties with pricing immediate annuities is that underwriting the annuitantis life is the exception rather than the rule. In the absence of underwriting, the price paid for a life-contingent annuity is the same for all sales at a given age. This exposes the market (insurance company and potential policyholder alike) to antiselection. The insurance company worries that only the healthiest people choose a life-contingent annuity and therefore adjust mortality accordingly. The potential policyholders worry that they are not being compensated for their relatively poor health and choose not to purchase what would otherwise be a very beneficial product. This paper develops a model of underlying, unobserved health. Health is a state variable that follows a first-order Markov process. An individual reaches the state “death” either by accident from any health state or by progressively declining health state. Health state is one-dimensional, in the sense that health can either “improve” or “deteriorate” by moving farther from or close to the “death” state, respectively. The probability of death in a given year is a function of health state, not of age. Therefore, in this model a person is exactly as old as he or she feels. I first demonstrate that a multistate, ageless Markov model can match the mortality patterns in the common annuity mortality tables. The model is extended to consider several types of mortality improvements: permanent through decreasing probability of deteriorating health, temporary through improved distribution of initial health state, and plateau through the effects of past health improvements. I then construct an economic model of optimal policyholder behavior, assuming that the policyholder either knows his or her health state or has some limited information. the value of mortality risk transfer through purchasing a life-contingent annuity is estimated for each health state under various risk-aversion parameters. Given the economic model for optimal purchasing of annuities, the value of underwriting (limited information about policyholder health state) is demonstrated. 相似文献
3.
Eric R. Ulm 《North American actuarial journal : NAAJ》2017,21(3):369-381
Guaranteed funds with crediting rates for fixed periods determined by a pension provider or insurance company are common features of accumulation annuity contracts. Policyholders can transfer money back and forth between these accounts and money market accounts that give them features similar to demand deposits, and yet they frequently credit a higher rate than the money market. Transfer restrictions are commonly employed to prevent arbitrage. In this article, we model the interaction between company and policyholder as a multiperiod game in which the company maximizes risk-neutral expected present value of profits and the policyholder maximizes his expected discounted utility. We find that the optimal strategy on the part of the company is to credit a rate higher than the money market rate in the first period to entice the policyholder to invest in the guaranteed fund. The company then credits the floor in the remaining periods as the policyholder transfers out the maximum amount. This does better for the policyholder in low interest rate environments and worse in high interest rate environments and acts as a type of “interest rate insurance” for the policyholder. 相似文献
4.
Carole Bernard Zhenyu Cui Steven Vanduffel 《North American actuarial journal : NAAJ》2017,21(1):63-86
In this article, we study the fair fee of a flexible premium variable annuity (FPVA), in which the policyholder can choose to pay periodic premiums during the accumulation phase instead of a single initial premium. We are able to express fair fees using a fast and accurate approximation based on bounds on the price of the FPVA. We identify scenarios that are particularly costly for the insurer. Our study could help insurers estimate the magnitude of typical underpricing when offering flexible-premium variable annuities with the same fee as the corresponding single-premium variable annuity. 相似文献
5.
Eric R. Ulm FSA 《North American actuarial journal : NAAJ》2013,17(1):16-37
Abstract Variable annuity contracts frequently include both guaranteed minimum death benefit (GMDB) options and options to transfer funds between fixed and variable accounts. We model the difference between fixed and variable rates as the primary determinant of policyholder transfer behavior. We find that people tend to transfer their money into variable accounts at about 39% of the rate that would be required to maintain constant percentage rebalancing, but with the opposite sign. If these transfers are not taken into account, the GMDB options on the variable accounts will be overvalued and overhedged. Ignoring this effect can have a substantial impact on the size of the futures portfolio needed to hedge this risk and a nonnegligible impact on the earnings of the variable annuity portfolio. 相似文献
6.
Manfred Wandt 《保险科学杂志》2011,100(4):445-459
This article analyzes the disputed legal nature of the duty to notify and the duty to disclose information according to sections 30 et seq. of the German Insurance Contract Act (VVG). To the extent to which the aforementioned legal provisions impose such obligations on a third party, the author reaches the conclusion that they are to be regarded as true legal obligations, i.e. their breach may result in damage claims. As to the policyholder, however, the legal provisions must be qualified as statutory warranties (so-called Obliegenheiten) without sanctions. Therefore, in order to sanction a policyholder’s breach of his obligations, the contracting parties have to turn the statutory Obliegenheiten into contractual Obliegenheiten, which are then subject to section 28 VVG. In the second part of the article the author addresses the scope of application and the content of the Obliegenheit to instruct the policyholder according to section 28 subsection 4 VVG. This Obliegenheit is imposed on the insurer as a requirement for the sanction of a breach of the contractual duties to provide information and to disclose by the policyholder. 相似文献
7.
Jungmin Choi 《North American actuarial journal : NAAJ》2017,21(2):281-296
We investigate the valuation problem of variable annuities with guaranteed lifelong/lifetime withdrawal benefit (GLWB) options, which give the policyholder the right to withdraw a specified amount as long as he or she lives, regardless of the performance of the investment. We assume the static approach that the policyholder’s withdrawal rate is a constant throughout the life of the contract. We apply the principle of equivalent utility to find the indifference price for a variable annuity with a GLWB contract with an equity-indexed death benefit. Using an exponential utility function, Hamilton-Jacobi-Bellman (HJB) type partial differential equations (PDEs) are derived for the pricing functions. We first assume the mortality is deterministic, and the pricing PDE is solved numerically using a finite difference method. The effects of various parameters are investigated, including the age at inception of the policyholder, withdrawal rate, risk-free rate, and volatility of the underlying asset. We also consider a roll-up option and analyze the effect of delaying the start of the withdrawals. Another pricing PDE is derived with a stochastic mortality, when the force of mortality is modeled with a stochastic differential equation. A finite difference method is used again to solve the pricing PDE numerically, and the sensitivities of the GLWB contracts with respect to the withdrawal rate and the risk-free rate are explored. 相似文献
8.
Daniel Bauer Jin Gao Thorsten Moenig Eric R. Ulm Nan Zhu 《North American actuarial journal : NAAJ》2017,21(4):485-501
The article presents a review of structural models of policyholder behavior in life insurance. We first discuss underlying drivers of policyholder behavior in theory and survey the implications of different models. We then turn to empirical behavior and appraise how well different drivers explain observations. The key contributions lie in the synthesis and the systematic categorization of different approaches. The article should provide a foundation for future studies, and we describe some important directions for future research in the conclusion. 相似文献
9.
This paper studies an optimal insurance and reinsurance design problem among three agents: policyholder, insurer, and reinsurer. We assume that the preferences of the parties are given by distortion risk measures, which are equivalent to dual utilities. By maximizing the dual utility of the insurer and jointly solving the optimal insurance and reinsurance contracts, it is found that a layering insurance is optimal, with every layer being borne by one of the three agents. We also show that reinsurance encourages more insurance, and is welfare improving for the economy. Furthermore, it is optimal for the insurer to charge the maximum acceptable insurance premium to the policyholder. This paper also considers three other variants of the optimal insurance/reinsurance models. The first two variants impose a limit on the reinsurance premium so as to prevent insurer to reinsure all its risk. An optimal solution is still layering insurance, though the insurer will have to retain higher risk. Finally, we study the effect of competition by permitting the policyholder to insure its risk with an insurer, a reinsurer, or both. The competition from the reinsurer dampens the price at which an insurer could charge to the policyholder, although the optimal indemnities remain the same as the baseline model. The reinsurer will however not trade with the policyholder in this optimal solution. 相似文献
10.
基于企业年金的人力资本管理功能,本文分析了实施年金计划对企业创新的影响及其机理,并以2007―2017年A股上市公司为样本进行了实证检验。研究结果表明,企业年金具有显著的创新激励效果,实施年金计划能够显著提高企业的创新水平。影响机理检验表明,企业年金能够通过增强员工满意度、加大对员工创新技能培训投入来发挥创新激励作用。进一步研究显示,企业年金对创新的积极影响具有一定持续性,并且在不同环境和企业特征下具有异质性,即企业年金对创新的促进作用仅体现在国有企业、处于市场竞争程度较高的企业以及处于成长期的企业。本文研究结论拓展了企业年金政策实施效果与企业创新影响因素的研究,为建立并完善企业年金计划、优化薪酬福利制度以实现创新引领企业高质量发展提供了经验支持。 相似文献
11.
S. J. Bjoraa 《Scandinavian actuarial journal》2013,2013(1):176-179
Premium return assurances are often connected with annuities, with various provisions. In the following it is assumed that the amount to be returned at the death of the annuitant is equal to the difference between the purchase money and the annuity payments that have been received. 相似文献
12.
Geoffrey Friesen 《The Journal of risk and insurance》2007,74(1):185-206
Stock insurers can reduce or eliminate agency conflicts between policyholders and stockholders by issuing participating insurance. Despite this benefit, most stock companies don't offer participating contracts. This study explains why. We study an equilibrium with both stock and mutual insurers in which stockholders set premiums to provide a fair expected return on their investment, and with a policyholder who chooses the insurance contract that maximizes her expected utility. We demonstrate that stockholders cannot profitably offer fully participating contracts, but can profitably offer partially participating insurance. However, when the policyholder participation fraction is high, the fair‐return premium is so large that the policyholder always prefers fully participating insurance from the mutual company. Policies with lower levels of policyholder participation are optimal for policyholders with relatively high risk aversion, though such policies are usually prohibited by insurance legislation. Thus, the reason stock insurers rarely issue participating contracts isn't because the potential benefits are small or unimportant. Rather, profitability or regulatory constraints simply prevent stock insurers from exercising those benefits in equilibrium. 相似文献
13.
给出保单持有人退保行为影响下的变额年金定价模型和对冲模型,当保单持有人分别采取无退保、固定退保和动态退保三种行为策略时,基于包含最低身故利益保证、最低满期利益保证和最低提取利益保证的三种不同的变额年金,运用蒙特卡罗模拟测试出保单持有人采取不同的退保策略对不同利益保证的变额年金风险对冲有着显著的不同影响。 相似文献
14.
Robert Koch 《保险科学杂志》2012,101(2):151-173
The article deals with the rights and obligations between the policyholder, the insured directors and officers of the policyholder and the insurer in ‘Insured vs. Insured’ D&;O claims. Based on a case study where several directors commit wrongful acts the following questions will be examined: (1) whether or not the policyholder is entitled to directly claim damages from the insurer, (2) whether or not the policyholder violates its duties towards the insurer or the insured directors by its deliberate choice not to make claims against all insured at the same time but in different policy periods, and (3) which obligations has the policyholder towards its directors when there is not sufficient coverage to cover all claims of the policyholder against the directors. 相似文献
15.
We introduce costly internal capital into a standard insurance model, in which a risk‐averse policyholder buys insurance from a risk‐neutral insurer with limited liability. The unique optimal contract and internal capital lead to a strictly positive probability for insurer default. Some risks are uninsurable in that the insurer chooses not to provide insurance against such risks. An increase in the cost of capital may lead to a higher optimal amount of internal capital. The results extend to multiple policyholders in a symmetric setting. Our extension of the classical model to include costly internal capital provides a fruitful approach to many real world insurance markets. 相似文献
16.
Kevin Dowd PhD David Blake PhD Andrew J. G. Cairns PhD 《North American actuarial journal : NAAJ》2013,17(2):237-247
Abstract This paper proposes a computationally efficient algorithm for quantifying the impact of interestrate risk and longevity risk on the distribution of annuity values in the distant future. The algorithm simulates the state variables out to the end of the horizon period and then uses a Taylor series approximation to compute approximate annuity values at the end of that period, thereby avoiding a computationally expensive “simulation-within-simulation” problem. Illustrative results suggest that annuity values are likely to rise considerably but are also quite uncertain. These findings have some unpleasant implications both for defined contribution pension plans and for defined benefit plan sponsors considering using annuities to hedge their exposure to these risks at some point in the future. 相似文献
17.
Runhuan Feng 《Quantitative Finance》2017,17(3):471-478
The guaranteed minimum withdrawal benefit (GMWB), which is sold as a rider to variable annuity contracts, guarantees the return of total purchase payment regardless of the performance of the underlying investment funds. The valuation of GMWB has been extensively covered in the previous literature, but a more challenging problem is the computation of the risk based capital for risk management and regulatory reasons. One needs to find the tail distribution of the profit–loss function, which differs from its expected payoff required for pricing the GMWB contract. GMWB has embedded two option-like features: Management fees are proportional to the current value of the policyholder’s account which results in an average price of the account. Thus the contract resembles an Asian option. However, the fees are charged only up to the time of the account hitting zero which resembles a barrier option payoff. Thus the GMWB is mathematically more complicated than Asian or barrier options traded on the financial markets. To the authors’ best knowledge, this is the first paper in the literature to formulate and analyse profit–loss distribution using PDE methods of such a product with intricate option-like features. Our approach is much more efficient than the current market practice of rather intensive and expensive Monte Carlo simulations due to the lack of samples for extreme cases. 相似文献
18.
ABSTRACTParticipating contracts provide a maturity guarantee for the policyholder. However, the terminal payoff to the policyholder should be related to financial risks of participating insurance contracts. We investigate an optimal investment problem under a joint value-at-risk and portfolio insurance constraint faced by the insurer who offers participating contracts. The insurer aims to maximize the expected utility of the terminal payoff to the insurer. We adopt a concavification technique and a Lagrange dual method to solve the problem and derive the representations of the optimal wealth process and trading strategies. We also carry out some numerical analysis to show how the joint value-at-risk and the portfolio insurance constraint impacts the optimal terminal wealth. 相似文献
19.
Hilger DD 《Benefits quarterly》2004,20(1):44-52
Employers that sponsor group health plans and serve as the plan administrator of those plans are required by the HIPAA Privacy Rule to execute business associate contracts with vendors that provide services on behalf of the plans. The business associate contracts must contain many specific provisions regarding the protection, use and disclosure of health information. This article looks at the implications of imposing business associate contract obligations on an integrated HR and benefits-outsourcing recordkeeper and cautions employers against an overly broad application of the requirements. 相似文献
20.
Petra Schumacher 《保险科学杂志》2008,97(1):71
The private annuity markets are traditionally small even though annuity products have many favorable properties from a theoretical point of view. In this paper, the discussed approaches to the so-called annuity puzzle are examined and evaluated. In particular, adverse selection has been repeatedly held responsible for the annuity puzzle. Thus, it is investigated if enhanced annuities can eliminate or reduce problems on the annuity markets caused by adverse selection. It is shown by a modeling approach that – depending on the superior knowledge of the insured – a first-best-solution can be implemented by offering enhanced annuities. 相似文献