跳扩散模型下权益指数年金的定价

权益指数年金收益在最小保证基础上, 能参与特定权益的收益. 通常权益指数年金定价是在假设权益指数遵从Black-Scholes模式下进行的, 但是一些例外事件(比如, 重大的政治事件)的发生, 会导致价格的巨幅波动, 这个假设并不合理. 因此本文研究了权益指数在跳扩散模型下权益指数年金的定价问题. 运用Esscher变换方法得到了点对点指数收益方法下权益指数年金定价的显示解,并对结果作了敏感性分析.     

用随机模拟法提留权益指数年金准备金

权益指数年金(Equity-Indexed Annuities)是一类新型年金产品,有最小收益保证,在最小保证基础上年金实际支付给保户的收益率与预先规定好的某类股票指数或债券指数收益相关联。本文研究了用随机模拟法提留权益指数年金准备金的问题,并分析了各参数对准备金的影响。     

带有Poisson跳的股票价格模型下权益指数年金的定价

本文考虑在死亡风险情况下,当股票指数服从Poisson跳扩散过程,缴费方式为等额年缴型的权益指数年金,分别给出在简单点对点和年度重设指数计算方法下该年金的定价公式,并对简单点对点方法下相关参数对参与率的影响进行分析.     

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．     

利率风险与或有权益定价

应用无差异方法研究不完全市场中或有权益的保值和定价问题,并证明了或有权益的价格不仅依赖于或有权益的不可复制部分,而且受利率风险的影响．在最优保值意义下利率风险分解为可控风险和不可控风险．利率的可控风险与资本市场波动有关,可通过套期保值方法避免,可能产生正、零或负的期望收益．利率的不可控风险与资本市场波动无关,无法对冲,而且带来正的期望收益．利率风险的分解有助于更准确地解释或有权益的价格-它受利率的不可控风险影响,而与可控风险无关．当利率的不可控收益与或有权益的不可复制部分正(负)相关时,或有权益的不可复制部分的风险越大导致或有权益的价格越高(低)．     

PLS情绪指数对中国股市风险收益关系的影响研究

从行为金融学角度研究投资者情绪对中国股市风险收益关系的影响,或有助于更好的解释风险收益关系.采用偏最小二乘法(PLS)构建新的投资者情绪综合指数,同时在对风险的度量中运用个股平均相关性代替总体方差来度量市场风险.研究结果表明PLS情绪指数比常用的主成分分析法所构建的情绪指数及单个情绪代理变量能更好的解释股市收益;平均相关性比市场波动更适合作为市场风险的度量指标;投资者情绪对风险收益关系有显著影响,其中在低情绪期风险和收益之间的相关性不显著,而高情绪期风险和收益之间呈现显著的负相关关系.由实证结果可知中国股市投资者存在非理性行为,应从行为金融的角度去考虑资产定价,同时对各指标的准确度量更有利于完善行为资产定价理论.     

敲定时间为随机变量的情况下奇异期权定价问题研究

受保险精算中定价最小死亡保证金的启发,当死亡发生时,会收到一定数额的财富作为补偿,而这笔财富当作是一种支付,它不仅依赖于原生资产的当前价格,还依赖于之前的价格信息.可以把这个支付函数看做是一种特殊期权的收益函数.又由于随机变量Tx(表示年龄为x的顾客从购买合约到死亡的时间段)的分布可以被近似地看做是几个指数分布的线性组合.假设股票价格变化服从双指数跳扩散过程.利用Lévy过程的指数停时的有关结果,给出敲定时间为随机变量的情况下累计期权的价格公式的显式解.这些定价方法可以用于与死亡相关的未定权益的定价,如各种养老金保险等.     

长寿风险对未来年金净保费的影响

本文深入地讨论了长寿风险对未来年金净保费的影响。一方面在随机死亡率预测的基础上,对未来年金净保费的概率分布特征进行研究,另一方面,基于年金定价的角度,在长寿风险存在的条件下比较了即期生存年金与延期生存年金二者的差异。     

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.     

随机利率情形下跳-扩散模型的未定权益定价

讨论Vasicek短期利率模型下,风险资产的价格过程服从跳-扩散过程的欧式未定权益定价问题,利用鞅方法得到了欧式看涨期权和看跌期权定价公式及平价关系,最后给出了基于风险资产支付连续红利收益的欧式期权定价公式.     

Optimal commutable annuities to minimize the probability of lifetime ruin

We find the minimum probability of lifetime ruin of an investor who can invest in a market with a risky and a riskless asset and who can purchase a commutable life annuity. The surrender charge of a life annuity is a proportion of its value. Ruin occurs when the total of the value of the risky and riskless assets and the surrender value of the life annuity reaches zero. We find the optimal investment strategy and optimal annuity purchase and surrender strategies in two situations: (i) the value of the risky and riskless assets is allowed to be negative, with the imputed surrender value of the life annuity keeping the total positive; (ii) the value of the risky and riskless assets is required to be non-negative. In the first case, although the individual has the flexibility to buy or sell at any time, we find that the individual will not buy a life annuity unless she can cover all her consumption via the annuity and she will never sell her annuity. In the second case, the individual surrenders just enough annuity income to keep her total assets positive. However, in this second case, the individual’s annuity purchasing strategy depends on the size of the proportional surrender charge. When the charge is large enough, the individual will not buy a life annuity unless she can cover all her consumption, the so-called safe level. When the charge is small enough, the individual will buy a life annuity at a wealth lower than this safe level.     

Optimal investment–consumption problem: Post-retirement with minimum guarantee

We study the optimal investment–consumption problem for a member of defined contribution plan during the decumulation phase. For a fixed annuitization time, to achieve higher final annuity, we consider a variable consumption rate. Moreover, to have a minimum guarantee for the final annuity, a safety level for the wealth process is considered. To solve the stochastic optimal control problem via dynamic programming, we obtain a Hamilton–Jacobi–Bellman (HJB) equation on a bounded domain. The existence and uniqueness of classical solutions are proved through the dual transformation. We apply the finite difference method to find numerical approximations of the solution of the HJB equation. Finally, the simulation results for the optimal investment–consumption strategies, optimal wealth process and the final annuity for different admissible ranges of consumption are given. Furthermore, by taking into account the market present value of the cash flows before and after the annuitization, we compare the outcomes of different scenarios.     

基于不等式约束的一类新的增广lagrangian函数

本文提出了一类新的增广lagrangian函数,并证明了它的稳定点、整体极小点与原约束问题KKT点、整体极小点有1-1对应关系,增广lagrangian函数的局部极小点为原问题的局部极小点.     

Portfolio Optimization With a Guaranteed Minimum Maturity Benefit and Risk-Adjusted Fees

Methodology and Computing in Applied Probability - We study a portfolio optimization problem involving the loss averse policyholder of a variable annuity with a guaranteed minimum maturity benefit....     

一类面积函数的最小值点的特性

本文运用Ｒｉｅｍａｎｎ－Ｓｔｉｅｌｊｅｏ积分的基本性质讨论了一类由连续单调函数所确定的面积函数的最小值问题，得到了该问题的最小值点恰为区问的中点。其变形问题的最小值点的函数值与函数在两端点的函数值的均值相等。     

分期付款期权在基于教育基金保险的期权中的应用

文献[1]提出了一种基于教育基金保险的欧式看涨期权,它赋予合约持有人在约定时间以约定价格购买连续支付固定年限的教育年金保险的权利,本文在[1]的基础上进一步提出基于教育基金保险的分期付款期权,该期权进一步改进了基于教育基金保险的欧式看涨期权,它赋予期权持有人分期支付期权费的权利,而不是一次性支付期权费,经过首期期权费的支付,期权持有人可以在继续支付期权费以持有期权和中断期权费的支付让期权作废之间选择,这样就可以使投资者在必要的时候取消期权,从而避免无效成本支出.该期权更加方便于低收入家庭和欲将资本用于其它高回报的投资的家庭进行教育投资.本文用后向递推和二叉树方法的方法给出期权定价公式,并确定分期支付的期权费的范围.     

尾年金分布的存在性和结构

本文主要是在年金分布的基础上, 推广、定义并研究了一类$r$尾年金分布的存在性和结构, 给出了这类分布的存在性条件, 证明了在一定条件下, $r$尾年金分布是年金分布与某一特殊$r$尾年金分布的混合.     

Government-provided annuities under insolvency risk

This paper seeks to determine whether governments should intervene in the private annuity market by directly providing public insurance in the form of annuities when both the government and the insurance companies could default. It is found that, although the government could default, intervening by means of an annuity can improve social welfare if the insurance companies could default and the expected return on the public annuity is greater than the rate of return on a risk-free bond. We also find that, under actuarially fair pricing, the government should provide more in terms of a public annuity than the optimal amount of the annuity that the individual purchases in the private market if the government is less likely to default on the public annuity than an insurance company would in the case of a private annuity.     

Government-provided annuities under insolvency risk

This paper seeks to determine whether governments should intervene in the private annuity market by directly providing public insurance in the form of annuities when both the government and the insurance companies could default. It is found that, although the government could default, intervening by means of an annuity can improve social welfare if the insurance companies could default and the expected return on the public annuity is greater than the rate of return on a risk-free bond. We also find that, under actuarially fair pricing, the government should provide more in terms of a public annuity than the optimal amount of the annuity that the individual purchases in the private market if the government is less likely to default on the public annuity than an insurance company would in the case of a private annuity.