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1.
We investigate the total time of deducting fees for variable annuities with state-dependent fee. This fee charging method is studied recently by Bernard et al. (2014) and Delong (2014) in which the fees deducted from the policyholder’s account depend on the account value. However, both of them have not considered the problem of analyzing probabilistic properties of the total time of deducting fees. We approximate the maturity of a general variable annuity contract by combinations of exponential distributions which are (weakly) dense in the space that is composed of all probability distributions on the positive axis. Working under general jump diffusion process, we derive analytic formulas for the expectation of the time of deducting fees as well as its Laplace transform.  相似文献   
2.
This paper introduces a class of unit-linked annuities that extends existing annuities by allowing portfolio shocks to be gradually absorbed into the annuity payouts. Consequently, our new class enables insurers to offer an affordable and adequate annuity with a stable payout stream. We show how to price and adequately hedge the annuity payouts in a general financial environment. In particular, our model accounts for various stylized facts of stock returns such as asymmetry and heavy-tailedness. Furthermore, the generality of our framework makes it possible to explore the impact of a parameter misspecification on the annuity price and the hedging performance.  相似文献   
3.
This paper proposes a technique to derive the optimal surrender strategy for a variable annuity (VA) as a function of the underlying fund value. This approach is based on splitting the value of the VA into a European part and an early exercise premium following the work of Kim and Yu (1996) and Carr et al. (1992). The technique is first applied to the simplest VA with GMAB (path-independent benefits) and is then shown to be possibly generalized to the case when benefits are path-dependent. Fees are paid continuously as a fixed percentage of the fund value. Our approach is useful to investigate the impact of path-dependent benefits on surrender incentives.  相似文献   
4.
In this paper we construct a framework to price the inflation-linked derivatives with the stochastic inflation rate, the stochastic interest rate, and stochastic risky assets with stochastic volatility. Because of the popularity of the guaranteed minimum death benefit (GMDB) in insurance market, we mainly study two types of GMDBs: the inflation guarantee and the combination guarantee. We consider the guaranteed minimum death benefit as an European option with a random maturity date, the closed-form pricing formulas for the GMDBs are derived by Fourier-based method. Moreover, we give an elaborate sensitivity analysis to explain economical behaviors of our models. The numerical results show that the death benefit of inflation guarantee is slightly overpriced in constant volatility of stock situation.  相似文献   
5.
安勇 《经济数学》2011,28(2):64-68
对于年金的时间价值的研究,往往假定利率在整个期间内是固定不变的,但事实上,由于受到多种因素的影响,利率通常具有不确定性.因此,本文采用可逆MA(1)模型对随机利息力进行建模,在此基础上,研究了期末付虹式年金和期末付平顶虹式年金的时间价值问题,给出了上述两种形式年金现值的期望和方差的递推公式.通过数值仿真分析了相关参数对...  相似文献   
6.
权益指数年金(Equity Indexed Annuities)是欧美市场近十年发展起来的一类新型年金产品,有最小收益保证,在最小保证基础上与预先设定好的某类股指收益相关联.本文在考虑死亡风险情况下,对简单点对点和年度重设两种指数计算方法下权益指数年金的定价问题作了研究,给出了定价公式并对参与率作了敏感性分析.  相似文献   
7.
Guaranteed annuity options are options providing the right to convert a policyholder’s accumulated funds to a life annuity at a fixed rate when the policy matures. These options were a common feature in UK retirement savings contracts issued in the 1970’s and 1980’s when interest rates were high, but caused problems for insurers as the interest rates began to fall in the 1990’s. Currently, these options are frequently sold in the US and Japan as part of variable annuity products. The last decade the literature on pricing and risk management of these options evolved. Until now, for pricing these options generally a geometric Brownian motion for equity prices is assumed. However, given the long maturities of the insurance contracts a stochastic volatility model for equity prices would be more suitable. In this paper explicit expressions are derived for prices of guaranteed annuity options assuming stochastic volatility for equity prices and either a 1-factor or 2-factor Gaussian interest rate model. The results indicate that the impact of ignoring stochastic volatility can be significant.  相似文献   
8.
We derive a number of analytic results for GMDB ratchet options. Closed form solutions are found for De Moivre’s Law, Constant Force of Mortality, Constant Force of Mortality with an endowment age and constant force of mortality with a cutoff age. We find an infinite series solution for a general mortality laws and we derive the conditions under which this series terminates. We sum this series for at-the-money options under the realistic Makeham’s Law of Mortality.  相似文献   
9.
我国的商业养老保险作为养老金体系的重要组成部分,在实践中的发展比较缓慢,原因之一是保险公司缺乏长寿风险管理的经验。本文将探索我国商业养老保险使用分红年金管理长寿风险的可行性。研究该分红年金在给付规则和分红来源方面的特征,并基于实际数据,构建动态随机死亡率模型和随机收益率模型,采用蒙特卡洛随机模拟方法,比较分红年金和传统年金在待遇分布、资产和损失分布、破产概率等方面的特征,得出分红年金能够在精算公平原则下有效应对长寿风险,并且在待遇给付、偿付能力和盈利能力方面具有明显优势的结论。  相似文献   
10.
In recent years, a market for mortality derivatives began developing as a way to handle systematic mortality risk, which is inherent in life insurance and annuity contracts. Systematic mortality risk is due to the uncertain development of future mortality intensities, or hazard rates. In this paper, we develop a theory for pricing pure endowments when hedging with a mortality forward is allowed. The hazard rate associated with the pure endowment and the reference hazard rate for the mortality forward are correlated and are modeled by diffusion processes. We price the pure endowment by assuming that the issuing company hedges its contract with the mortality forward and requires compensation for the unhedgeable part of the mortality risk in the form of a pre-specified instantaneous Sharpe ratio. The major result of this paper is that the value per contract solves a linear partial differential equation as the number of contracts approaches infinity. One can represent the limiting price as an expectation under an equivalent martingale measure. Another important result is that hedging with the mortality forward may raise or lower the price of this pure endowment comparing to its price without hedging, as determined in Bayraktar et al. (2009). The market price of the reference mortality risk and the correlation between the two portfolios jointly determine the cost of hedging. We demonstrate our results using numerical examples.  相似文献   
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