随机利率下的一类特殊年金

研究在随机利率相互独立条件下的某些延付年金的积累值的计算问题,目的在于研究积累值的期望和方差.研究了在随机利率相互独立条件下的期末付虹式年金,期末付平顶虹式年金,期末付倒虹式年金和期末付倒平顶虹式年金的积累值的期望和方差,并且给出了积累值的期望和方差的计算公式.     

一类随机利率下特殊年金的计算

研究在随机利率相互独立条件下年金初值的计算问题,主要是研究各类年金初值的期望和方差的计算公式.文章给出了随机利率相互独立条件下期末付平顶虹式年金,期末付虹式年金,期末付倒平顶虹式年金和期末付倒虹式年金的初值公式及其简化关系,推导出了这类年金初值的各阶矩的简化公式,进而获得了这类年金初值的期望计算公式和方差计算公式.     

随机利息力下的期末付倒平顶虹式年金

对于年金的定价问题的研究,传统精算理论假定利率是恒定不变的．但事实上,由于受到多种因素的影响,利率往往具有不确定性．因此,本文采用可逆MA（1）模型来刻画利率期限机构,在此基础上,研究了期末付倒平顶虹式年金的各阶矩问题,推导出了其年金现值的期望和方差的简洁公式．通过数值模拟分析了此年金面临的利率风险,其结论对年金定价有一定的参考价值．     

一类随机利率模型下的年金精算现值

年金在日常生活中被广泛应用,但已往大多研究的是固定年金以及随机利率下的确定年金.本文在前人研究成果的基础上考虑了利率随机波动对生命年金的影响,运用随机利率模型,得出年金精算现值较为简单的递推关系式,并举例说明利率的随机波动对年金精算现值的影响程度,结果表明利率的波动对年金的定价影响非常大,绝对不容忽视.     

随机利率下年金的时间价值

本文首先在常数利率下讨论了递增年金、递减年金和固定增长年金的终值.进而在随机利率条件下研究了递增年金、递减年金和固定增长年金,得到了递增年金、递减年金和固定增长年金终值的期望与方差,推广了Zaks(2001)的结果.     

基于广义条件AR(p)利率下的生存年金精算现值模型及其应用

本文利用时间序列理论将投资利率为条件 AR(p)模型推广为广义条件 AR(p)模型 ,得到利息力模型的一阶矩和二阶矩 ;针对年末支付的定期生存年金 ,利用生存年金理论得到广义条件 AR(p)利率模型下生存年金的精算现值模型 ,这对保险人合理制定保费标准和规避风险等问题具有重要理论指导意义和实际应用价值 .     

随机利率下的年金的计算

我们考虑随机利率下的一类延付年金在n年后的积累值的计算问题,目的在于研究积累值的期望和方差.本文给出两种方法计算在某些年内一类延付年金的积累值的期望和方差,获得了积累值的方差的递推关系,并且给出了计算公式.     

基于Lee-Carter模型的互助养老年金研究

基于经典的双线性随机Lee-Carter模型,采用经济学的协整理论,对中国大陆男性人口死亡率进行预测,克服了ARIMA模型预测的局限性.在随机利率和Lee-Carter模型的基础上度量退休年金和生命年金的长寿风险,并为此提出应对策略,引入由消费者承担系统长寿风险、年金池承担个体长寿风险的群体自助养老年金(GSA),然后对其进行实证分析发现,与普通年金相比,GSA模型分担模式拥有较高的给付额.     

随机利率下的连续型生存年金

本文首次以连续型生存年金为对象,采用Wiener过程对利息力累积函数建模,得到了该利率模型下的连续型生存年金现值的各阶矩,并在一些特殊条件下得到了矩的简单表达式.     

一类随机利率下的确定年金

我们考虑在一定的约束条件下利率是随机变量的某些确定年金的现值的计算问题,目的在于研究给付现值的期望和方差.本文给出两种方法计算在某些年内一类延付年金的现值之和的期望和方差,获得了给付现值的方差的递推关系,并且解决了这些关系,这在计算简单方面明显地更好.     

Using the Black–Derman–Toy interest rate model for portfolio optimization

No-arbitrage interest rate models are designed to be consistent with the current term structure of interest rates. The diffusion of the interest rates is often approximated with a tree, in which the scenario-dependent fair price of any security is calculated as the present value of the risk-neutral expectation by backward induction. To use this tree in a portfolio optimization context it is necessary to account for the so-called “market price of risk”. In this paper we present a method to change the conditional probabilities in the Black–Derman–Toy model to the physical (or real) measure, including the market price of risk, and explore the economic implications for expected spot rates and for expected bond returns.     

随机利率下的增额寿险模型研究

在实际的保险精算中,保单保险金现值函数的期望就是该种保单的纯保费,而方差常用来度量该种保单的风险.对随机利率采用W iener过程建模,得到了增额寿险保险金现值函数的期望和方差.     

Pricing European Options in a Discrete Time Model for the Limit Order Book

In this paper we build a discrete time model for the structure of the limit order book, so that the price per share depends on the size of the transaction. We deduce the value of a portfolio when the investor trades using market orders and a bank account with different interest rates for lending and borrowing. We also deduce conditions to rule out arbitrage and solve the problem of pricing and hedging an European call option with physical delivery. It is shown that contrary to the perfectly liquid setting, the price of a European call is not given by an expectation, but can be expressed as an optimization problem on a set of equivalent probability measures.

     

状态转移下的利率预期与误差学习假说

采用线性回归和状态转移模型讨论利率预期的"误差学习假说"和不同期限利率预测误差之间的关联性,并考虑带有风险溢价时预测误差的作用.分析发现,1年期限的"误差学习假说"在银行间国债市场中是成立的,不同期限的利率预期对预测误差的反应呈现一定的独立性,不同的状态中预测误差和风险溢价对利率预期的影响是不同的,考虑风险溢价有助于提升对利率预期变动的解释.     

有限状态多期模型下的最小熵等价鞅测度及其应用

采用有限状态多期模型描述股票价格变动过程,导出了有红利支付情形下的最小熵等价鞅测度,给出了股票价格变动趋势的风险中性预期与红利率和无风险利率之间相对大小的关系,从理论上证明了无风险利率大于股票红利率时,市场将呈现出一种向上的风险中性趋势;无风险利率小于股票红利率时,市场将呈现出一种向下的风险中性趋势;无风险利率等于红利率时,股票价格将围绕初始价格上下波动而没有明显的风险中性趋势.     

Optimal dividends and bankruptcy procedures: Analysis of the Ornstein-Uhlenbeck process

This paper investigates the impact of bankruptcy procedures on optimal dividend barrier policies. We specifically focus on Chapter 11 of the US Bankruptcy Code, which allows a firm in default to continue its business for a certain period of time. Our model is based on the surplus of a firm that earns investment income at a constant rate of credit interest when it is in a creditworthy condition. The firm pays a debit interest rate that depends on the deficit level when it is in financial distress. Thus, the surplus follows an Ornstein-Uhlenbeck (OU) process with a negative surplus-dependent mean-reverting rate. Default and liquidation are modeled as distinguishable events by using an excursion time or occupation time framework. This paper demonstrates how the optimal dividend barrier can be obtained by deriving a closed-form solution for the dividend value function. It also characterizes the distributional property and expectation of bankruptcy time subject to the bankruptcy procedure. Our numerical examples show that under an optimal dividend barrier strategy, the bankruptcy procedure may not prolong the expected bankruptcy time in some situations.     

Expected present value of total dividends in a delayed claims risk model under stochastic interest rates

In this paper, a compound binomial risk model with a constant dividend barrier under stochastic interest rates is considered. Two types of individual claims, main claims and by-claims, are defined, where every by-claim is induced by the main claim and may be delayed for one time period with a certain probability. In the evaluation of the expected present value of dividends, the interest rates are assumed to follow a Markov chain with finite state space. A system of difference equations with certain boundary conditions for the expected present value of total dividend payments prior to ruin is derived and solved. Explicit results are obtained when the claim sizes are K_n distributed or the claim size distributions have finite support. Numerical results are also provided to illustrate the impact of the delay of by-claims on the expected present value of dividends.     

Using fuzzy random variables in life annuities pricing

This paper develops life annuity pricing with stochastic representation of mortality and fuzzy quantification of interest rates. We show that modelling the present value of annuities with fuzzy random variables allows quantifying their expected price and risk resulting from the uncertainty sources considered. So, we firstly describe fuzzy random variables and define some associated measures: the mathematical expectation, the variance, distribution function and quantiles. Secondly, we show several ways to estimate the discount rates to price annuities. Subsequently, the present value of life annuities is modelled with fuzzy random variables. We finally show how an actuary can quantify the price and the risk of a portfolio of annuities when their present value is given by means of fuzzy random variables.     

Optimal dividends and bankruptcy procedures: Analysis of the Ornstein–Uhlenbeck process

This paper investigates the impact of bankruptcy procedures on optimal dividend barrier policies. We specifically focus on Chapter 11 of the US Bankruptcy Code, which allows a firm in default to continue its business for a certain period of time. Our model is based on the surplus of a firm that earns investment income at a constant rate of credit interest when it is in a creditworthy condition. The firm pays a debit interest rate that depends on the deficit level when it is in financial distress. Thus, the surplus follows an Ornstein–Uhlenbeck (OU) process with a negative surplus-dependent mean-reverting rate. Default and liquidation are modeled as distinguishable events by using an excursion time or occupation time framework. This paper demonstrates how the optimal dividend barrier can be obtained by deriving a closed-form solution for the dividend value function. It also characterizes the distributional property and expectation of bankruptcy time subject to the bankruptcy procedure. Our numerical examples show that under an optimal dividend barrier strategy, the bankruptcy procedure may not prolong the expected bankruptcy time in some situations.