Vasicek利率与Heston模型下的最优投资和再保险

本文主要研究Vasicek随机利率模型下保险公司的最优投资与再保险问题.假设保险公司的盈余过程由带漂移的布朗运动来描述,保险公司通过购买比例再保险来转移索赔风险;同时,将财富投资于由一种无风险资产与一种风险资产组成的金融市场,其中,利率期限结构服从Vasicek利率模型,且风险资产价格过程满足Heston随机波动率模型.利用动态规划原理及变量替换的方法,得到了指数效用下最优投资与再保险策略的显示表达式,并给出数值例子分析了主要模型参数对最优策略的影响.     

Heston模型下的方差互换定价研究

通过实证分析论证了波动率具有均值回复性质的合理性.在Heston模型下,利用Ito积分推导出了方差互换在其存续期内任意时刻的价格与公平执行价格的定价公式.得到公平执行价格是波动率的平方的初始水平与长期均值水平的线性组合的性质,并利用该性质对Heston模型参数的敏感性进行了分析.     

基于Volterra Heston模型的最优投资和再保险问题

作为金融市场体系的重要组成部分,选择最优的投资和再保险策略对保险公司来说十分重要.本文研究了保险公司在均值-方差准则下的最优投资和再保险问题,假设保险公司通过购买比例再保险来分散自身风险,其盈余过程由近似经典Cramer-Lundberg模型的扩散过程刻画,此外,保险公司通过投资于无风险资产和风险资产来增加收入,其中风险资产价格服从Volterra Heston模型.由于Volterra Heston模型的非马尔可夫性和非半鞅性,经典的随机最优控制框架不再适用,本文通过构造一个辅助随机过程,得到了依赖于Riccati-Volterra方程解的最优投资和再保险策略及有效前沿,并对最优策略、有效前沿和波动率粗糙度、再保险因素之间的关系进行了数值分析,发现股票价格的波动率越粗糙,保险公司对股票市场和再保险的需求越大.     

养老基金投资组合的常方差弹性(CEV)模型和解析决策

针对以年金形式发放待遇的缴费预定制养老基金,在退休前和退休后的两个阶段,分别构建了常方差弹性(CEV)模型,并应用Legendre变换将原问题转化为对偶问题,在追求指数效用最大化的条件下,求得了精确解析解,从而确定了这两个阶段的最优投资决策．     

基于Heston随机波动率模型和风险偏好视角的资产负债管理

本文研究基于Heston随机波动率模型的资产负债管理问题。假设金融市场由一个无风险资产和一个风险资产构成,投资者的目标是最大化其终端财富的期望效用。应用随机控制方法,得到了该问题最优资产配置策略的解析表达式和相应值函数的解析解,通过数值算例分析了Heston模型主要参数以及债务对最优资产配置策略的影响。结果表明:配置到风险资产的比例对Heston模型中的参数非常敏感;为了对冲债务风险,负债的引入使得配置到风险资产的比例比无负债情形下的高;在风险厌恶系数变大时,无论投资者是否有负债,其投资到风险资产的比例则越来越低。     

Heston随机波动率市场中带VaR约束的最优投资策略

本文研究了Heston随机波动率市场下, 基于VaR约束下的动态最优投资组合问题。
假设Heston随机波动率市场由一个无风险资产和一个风险资产构成,投资者的目标为最大化其终端的期望效用。与此同时, 投资者将动态地评估其待选的投资组合的VaR风险,并将其控制在一个可接受的范围之内。本文在合理的假设下,使用动态规划的方法,来求解该问题的最优投资策略。在特定的参数范围内,利用数值方法计算出近似的最优投资策略和相应值函数, 并对结果进行了分析。     

Heston随机方差模型下确定缴费型养老金的最优投资

本文对确定缴费计划养老金的最终财富期望指数效用最大的最优投资组合进行研究.假设养老金计划的基金可以投资于无风险资产和风险资产,并且风险资产的方差服从Heston模型,得到最优投资和最大期望指数效用的明确表达式.此外,通过数值计算还得到最优投资与各个参数之间的关系.     

Heston随机波动模型时变利率下支付红利的timer期权定价

本文研究了在Heston随机波动模型下,连续支付红利的timer期权定价的条件Black-Scholes-Merton型公式.首先,利用投资组合的?-对冲原理构造无风险资产,给出了timer期权在Heston随机波动模型下所满足的偏微分方程.然后利用拉普拉斯逆变换得到了与贝塞尔过程相关的联合密度函数的显式公式.最后得到支付红利下timer期权定价的Black-Scholes-Merton型公式.     

固定支付下养老基金资产组合CEV模型及最优投资策略

在固定支付水平的条件之下,就养老基金资产组合问题建立常方差弹性(CEV)模型,应用随机控制原理求出了相应的非线性Hamilton-Jacobi-Bellman偏微方程,再用Legendre变换将其转化为线性偏微方程,建立对偶问题.通过对偶问题的求解,从而求得原问题的精确解析解,确定风险资产和无风险资产的最优投资比例,实现了满足养老基金既定支出水平下总资产的对数效用最大化,从实际市场的角度改进发展了经典的Merton模型结果.     

Risk measurement and management of defined benefit pension schemes: a stochastic approach

The traditional actuarial valuation for defined benefit pensionschemes operates on the basis of a set of deterministic calculationscombined with actuarial judgment. It has played an importantrole in guiding decision-making as far as the level of fundingis concerned. The paper argues that stochastic methods can addvalue in certain crucial areas, in particular the financialrisk management of such schemes. The traditional approach torisk is to incorporate margins in the valuation assumptions;however, a stochastic approach allows the user to evaluate specificand quantifiable risk and performance measures in respect ofalternative funding and investment strategies. The paper introducesa framework that measures the risks inherent in asset allocationand contribution rate decisions, allowing decisions to be madeon a more informed basis. In doing this, we suggest and applysome potential risk and performance measures. This frameworkprovides the means to explore the trade-offs involved in possiblecontribution and asset allocation decisions and leads to decisionstrategies that are expected to give improved outcomes for thesame level of risk. A realistic case study is used to illustratethe properties of the methodology and how it might be used.     

The Heston model with stochastic elasticity of variance

Empirical evidence suggests that single factor models would not capture the full dynamics of stochastic volatility such that a marked discrepancy between their predicted prices and market prices exists for certain ranges (deep in‐the‐money and out‐of‐the‐money) of time‐to‐maturities of options. On the other hand, there is an empirical reason to believe that volatility skew fluctuates randomly. Based upon the idea of combining stochastic volatility and stochastic skew, this paper incorporates stochastic elasticity of variance running on a fast timescale into the Heston stochastic volatility model. This multiscale and multifactor hybrid model keeps analytic tractability of the Heston model as much as possible, while it enhances capturing the complex nature of volatility and skew dynamics. Asymptotic analysis based on ergodic theory yields a closed form analytic formula for the approximate price of European vanilla options. Subsequently, the effect of adding the stochastic elasticity factor on top of the Heston model is demonstrated in terms of implied volatility surface. Copyright © 2016 John Wiley & Sons, Ltd.     

Some current issues in accounting for the cost of defined benefit pension schemes

This paper discusses the issues underlying the InternationalAccounting Standards Board (IASB)'s review of accounting forpension obligations. Pension obligations are currently dealtwith by International Accounting Standard 19. This containsthree important features, which are currently under review:(1) A smoothing mechanism (the ‘corridor’) for recognizingactuarial gains and losses. (2) An expected rate of return onplan assets, which is different from the actual (achieved) return.(3) An asset ceiling, which limits the extent to which surplusplan assets are recognized in the accounts of the employer.The IASB's current thinking on these issues is explained, andcomparisons are made with the UK's controversial Financial ReportingStandard 17. The paper concludes with a brief discussion oftwo important aspects of measuring defined benefit obligationsthat are not being considered in the present review.     

Minimization of risks in defined benefit pension plan with time‐inconsistent preferences

In this paper, we investigate the defined benefit pension plan, where the object of the manager is to minimise the contribution rate risk and the solvency risk by considering a quadratic performance criterion. To incorporate some well‐documented behavioural features of human beings, we consider the situation where the discounting is non‐exponential. It leads to a time‐inconsistent control problem in the sense that the Bellman optimality principle does no longer hold. In our model, we assume that the benefit outgo is constant, and the pension fund can be invested in a risk‐free asset and a risky asset whose return follows a geometric Brownian motion. We characterise the time‐consistent strategies and value function in terms of the solution of a system of integral equations. The existence and uniqueness of the solution is verified, and the approximation of the solution is obtained. Some numerical results of the equilibrium contribution rate and equilibrium investment policy are presented for three types of discount functions. Copyright © 2015 John Wiley & Sons, Ltd.     

Analytic approach to solve a degenerate parabolic PDE for the Heston model

We present an analytic approach to solve a degenerate parabolic problem associated with the Heston model, which is widely used in mathematical finance to derive the price of an European option on an risky asset with stochastic volatility. We give a variational formulation, involving weighted Sobolev spaces, of the second‐order degenerate elliptic operator of the parabolic PDE. We use this approach to prove, under appropriate assumptions on some involved unknown parameters, the existence and uniqueness of weak solutions to the parabolic problem on unbounded subdomains of the half‐plane. Copyright © 2017 John Wiley & Sons, Ltd.     

Optimal investment strategy for annuity contracts under the constant elasticity of variance (CEV) model

This paper focuses on the constant elasticity of variance (CEV) model for studying the optimal investment strategy before and after retirement in a defined contribution pension plan where benefits are paid under the form of annuities; annuities are supposed to be guaranteed during a certain fixed period of time. Using Legendre transform, dual theory and variable change technique, we derive the explicit solutions for the power and exponential utility functions in two different periods (before and after retirement). Each solution contains a modified factor which reflects an investor’s decision to hedge the volatility risk. In order to investigate the influence of the modified factor on the optimal strategy, we analyze the property of the modified factor. The results show that the dynamic behavior of the modified factor for the power utility mainly depends on the time and the investor’s risk aversion coefficient, whereas it only depends on the time in the exponential case.     

贝叶斯方法在养老基金资产负债管理中的应用

把一个静态资产负债管理模型———均值方差模型应用到定额给付养老金计划的资产负债管理中,在允许无风险借贷的条件下研究养老金在无风险资产和风险资产间的分配问题,用定量分析的方法求出了最优投资组合的一般形式;又针对投资收益率特征参数未知的情况,提出了矩估计和贝叶斯估计两种方法求解最优资本配置比例,将两种方法的结果与一般形式对比,分析了影响最优投资组合的因素,得知养老基金在风险资产中的投资比例与基金经理对风险的厌恶程度、风险资产的风险益酬、风险资产收益率的波动性成负相关关系;并且随决策者掌握的历史信息增加,在风险资产上的投资比例也随之增加,投资行为逐渐趋于理性化;对上述结果进行仿真,验证了结论的有效性。