一类含消费、寿险和投资的随机最优控制问题

本文研究在CRRA(constant relative risk aversion)效用下,关于消费、寿险和投资的随机最优控制问题.投资者可以投资于零息债券、股票和寿险.假设利率模型是Vasicek模型,股票模型是广义Heston随机波动率模型.此外,用Black-Scholes模型刻画收入项,且收入的增长率与利率有协整关系.通过动态规划的方法和解对应的HJB(Hamilton-Jacobi-Bellman)方程的技术得到最优策略.为了探索各个经济参数对最优策略的影响,本文给出数值分析.     

国内旅游消费与经济增长的变结构协整分析

考虑到数据结构突变可能导致国内旅游消费与经济增长之间的关系发生变化,选取1990-2011年的数据,运用变结构协整理论和误差修正模型对国内旅游消费与经济增长的关系进行实证分析,并与不考虑结构突变的模型进行比较.实证结果表明:国内旅游消费与经济增长之间的协整关系在1993年和2003年分别发生了状态开关型与水平趋势项漂移,且考虑结构突变的模型具有更好的样本拟合效果.     

中国碳排放与能源消费关系实证研究——基于VEC模型

中国碳减排问题成为世界关注的焦点问题.研究碳排放与能源消费关系有助于实现2020年碳减排目标.选取1953-2008年中国碳排放和能源消费数据,运用协整理论、向量误差修正模型(VEC)和Granger因果关系分析,对中国碳排放量与能源消费之间的相互关系进行实证研究.研究结果表明:碳排放与能源消费之间存在协整关系,能源消费增加1%,碳排放将增加0.9646%,即碳排放对能源消费的长期弹性为0.9646.从短期误差修正模型来看,碳排放与能源消费之间具有动态调整机制.非均衡误差项的存在,能够保证两者之间长期均衡关系的存在.Granger因果关系研究表明:碳排放与能源消费之间互为双向因果关系.通过脉冲函数和方差分解分析了模型的动态特征.根据研究结果,提出降低能源消费和减少碳排放对策.     

带线性时间趋势的分位数回归协整模型检验

协整检验是进行回归分析的首要过程,是避免伪回归的主要方法.然而,大多数协整检验技术都是建立在非稳健的普通最小二乘框架下.这对于普遍具有尖峰厚尾的时间序列来说,可能会导致统计检验的失效.为了解决这个困难,本文提出带线性时间趋势模型的分位数回归协整检验方法.不同于传统的静态协整分析,我们构建了一个分位数残差累积和(QCS)统计量来检验不同分位点上变量间的动态协整关系.应用分位数回归和泛函极限理论,推导出了统计量的渐近分布,并提出了修正的QCS统计量,拓展了其在序列相关以及长期内生性模型中的应用.模拟给出了统计量的临界值并证明了本文的协整检验方法具有良好的有限样本性质.最后,利用所提方法,检验了可支配收入与实际消费之间的动态协整关系,发现随着分位点的增大,它们之间的协整关系越强.     

我国农民消费问题的分省面板协整模型分析

依据现代消费理论,在符合中国经济现实假设条件下,建立了我国农民消费问题的数理函数。使用1980-2006年的宏观消费数据,通过协整模型分析表明我国农民的边际消费倾向约为0.69;基于Hausman检验的固定效应模型的面板单位根和面板协整对我国30个省份分析结果表明边际消费倾向为0.7;变截距变斜率面板模型表明各省的长期自主消费和长期边际消费倾向差异显著,上海、江苏呈现双高特征,吉林、海南和西藏则呈现双低特征,其他省份则表现为自主消费和边际消费倾向两者此高彼低的特点。差异产生的原因在于消费习惯不同以及收入差异导致的"主动、被动"消费造成的结果,提出了为西部增收以促进消费良性循环的合理的政策建议。     

能源消费与产业发展的协整性与因果关系分析

能源消费与经济增长关系密切,本文利用协整理论,检验了我国能源消费总量与国民生产总值以及三次产业之间的协整性和Granger因果关系,并且建立了向量误差修正模型。研究结果表明,我国能源消费与GDP以及第一产业、第三产业之间存在协整关系,但是能源消费与第二产业之间并不存在长期的均衡关系。并且,GDP和三次产业只是能源消费的单向Granger因果关系,它们之间并不存在双向的Granger因果关系。     

基于变结构协整方法的房地产市场与证券市场关联性分析

运用变结构协整方法,对房地产市场与证券市场相关指数进行了实证分析,结果显示:在所考虑的数据区间房屋销售价格指数与地产指数存在变结构协整关系.同时讨论了变结构模型的应用效果,最后给出了一些相关的建议.     

随机利率条件下最优投资消费与寿险购买策略

随着我国利率市场化的深入发展, 利率的随机波动对投资者的最优投资消费策略将产生重要影响. 与此同时, 随着我国寿险市场的渐趋完善, 寿险购买也越来越受到投资者的重视, 投资者的最优策略也将发生改变. 现研究由 Vasicek 模型来刻画的随机利率条件下最优投资消费与寿险购买策略. 投资者的目标在于选择最优投资消费与寿险购买策略使期望效用最大化. 通过运用 Legendre 转换方法求出最优投资消费与寿险购买的显性解. 通过数值分析的方法, 实证分析相关变量的变化对投资者最优投资与寿险购买策略的影响.     

我国经济增长与利用外资的变结构协整分析

本文分析了我国利用外资与经济增长之间的关系。运用协整分析方法,考虑数据结构突变的可能性,本文研究发现,对结构突变的数据序列,恩格尔—葛兰杰检验没有检测到协整关系;通过设定虚拟变量,成功检测到该协整关系,并建立误差修正模型。基于现有数据的实证结果表明我国经济增长与利用外资之间的协整关系在1997年发生了变化。     

基于变结构协整方法的期货市场与证券市场关联性分析——沪深300股指期货与沪深300指数的实证分析

对我国沪深300指数与沪深300指数期货的周数据进行了关联性分析.首先利用EG检验和Johansen系统检验对两指数进行协整检验,然后通过3种变结构协整模型分别检验,结果找到了变点,得到了变机构长期均衡关系和误差修正模型,同时比较了4种模型的应用效果,给出了相关的政策建议.     

广西能源、环境和经济增长的动态关系研究——基于VAR模型的实证分析

利用广西1990-2011年GDP、能源消费和工业废气排放总量的数据,应用基于VAR模型的动态计量分析方法,对广西经济、能源和环境的关系进行实证研究.结果表明:三者之间存在长期稳定的协整关系,能源消耗是经济增长和环境污染的Granger原因,经济增长是能源消耗和环境污染的Granger原因.能源消耗对经济增长的正向影响效应时间较长且较稳定,环境污染初期对经济增长的抑制作用较弱却呈现缓慢增强的趋势;而经济增长对能源消耗和环境污染的影响持续时间较短.经济增长与能源消耗两者之间的相互影响较大,而环境污染受能源消耗变化影响较明显.     

Household consumption, investment and life insurance

This paper develops a continuous-time Markov model for utility optimization of households. The household optimizes expected future utility from consumption by controlling consumption, investments and purchase of life insurance for each person in the household. The optimal controls are investigated in the special case of a two-person household, and we present graphics illustrating how differences between the two persons affect the controls.     

Purchasing life insurance to reach a bequest goal

We determine how an individual can use life insurance to meet a bequest goal. We assume that the individual’s consumption is met by an income from a job, pension, life annuity, or Social Security. Then, we consider the wealth that the individual wants to devote towards heirs (separate from any wealth related to the afore-mentioned income) and find the optimal strategy for buying life insurance to maximize the probability of reaching a given bequest goal. We consider life insurance purchased by a single premium, with and without cash value available. We also consider irreversible and reversible life insurance purchased by a continuously paid premium; one can view the latter as (instantaneous) term life insurance.     

Mean–variance asset–liability management: Cointegrated assets and insurance liability

The cointegration of major financial markets around the globe is well evidenced with strong empirical support. This paper considers the continuous-time mean–variance (MV) asset–liability management (ALM) problem for an insurer investing in an incomplete financial market with cointegrated assets. The number of trading assets is allowed to be less than the number of Brownian motions spanning the market. The insurer also faces the risk of paying uncertain insurance claims during the investment period. We assume that the cointegration market follows the diffusion limit of the error-correction model for cointegrated time series. Using the Markowitz (1952) MV portfolio criterion, we consider the insurer’s problem of minimizing variance in the terminal wealth, given an expected terminal wealth subject to interim random liability payments following a compound Poisson process. We generalize the technique developed by Lim (2005) to tackle this problem. The particular structure of cointegration enables us to solve the ALM problem completely in the sense that the solutions of the continuous-time portfolio policy and efficient frontier are obtained as explicit and closed-form formulas.     

基于计量经济模型的煤炭消费与经济增长关系实证研究——以世界主要煤炭消费国为例

经济的发展和能源(包括煤炭)的利用有着密不可分的关系.运用国际上研究能源消费与经济增长之间关系的重要工具-协整分析、格兰杰因果关系检验对世界主要煤炭消费国家(中国、美国、印度、俄罗斯、日本和南非)1981-2005的煤炭消费与GDP之间因果关系及其内在规律进行了分析和研究.实证研究结果表明,这些国家能源消费结构、经济政策不同,煤炭消费同经济增长之间的因果关系也不完全一致,中国、日本和南非存在经济增长对煤炭消费的因果关系,俄罗斯存在煤炭消费对经济增长的因果关系,而印度煤炭消费和经济增长之间则不存在因果关系.据此各国根据自身能源国情及国际比较形势,制定科学的能源战略与政策.     

To borrow or insure? Long term care costs and the impact of housing

We assess the impact of housing, the availability of reverse mortgages and long-term care (LTC) insurance on a retiree’s optimal portfolio choice and consumption decisions using a multi-period life cycle model that takes into consideration individual longevity risk, health shocks and house price risk. We determine how much an individual should borrow against their home equity and how much to insure health care costs with LTC insurance. We introduce an endogenous grid method, along with a regression based approach, to improve computational efficiency and avoid the curse of dimensionality. Our results confirm that borrowing against home equity provides higher consumption in earlier years and longevity insurance. LTC insurance transfers wealth from healthy states to disabled states, but reduces early consumption because of the payment of insurance premiums. Housing is an illiquid asset that is important in meeting bequest motives, and it reduces the demand for LTC insurance for the wealthy. We show that the highest welfare benefits come from combining a reverse mortgage with LTC insurance because of strong complementary effects between them. This result highlights the benefits of innovative products that bundle these two products together.     

Deterministic mean-variance-optimal consumption and investment

In dynamic optimal consumption–investment problems one typically aims to find an optimal control from the set of adapted processes. This is also the natural starting point in case of a mean-variance objective. In contrast, we solve the optimization problem with the special feature that the consumption rate and the investment proportion are constrained to be deterministic processes. As a result we get rid of a series of unwanted features of the stochastic solution including diffusive consumption, satisfaction points and consistency problems. Deterministic strategies typically appear in unit-linked life insurance contracts, where the life-cycle investment strategy is age dependent but wealth independent. We explain how optimal deterministic strategies can be found numerically and present an example from life insurance where we compare the optimal solution with suboptimal deterministic strategies derived from the stochastic solution.     

Health shock risk,critical illness insurance,and housing services

This paper studies a consumption–investment problem involving health shock risk, perishable consumption, and consumption of housing services. Additionally to a risk-free asset and a stock index, the agent can invest in real estate. I analyze the impact of health shocks on the optimal consumption and investment decisions in model specifications with and without the possibility to buy critical illness insurance. I discuss the influence of critical illness insurance on the optimal strategy and analyze the drivers of the optimal critical illness insurance demand. The results indicate that health shock risk has potentially devastating consequences, especially for young agents. It turns out that critical illness insurance is an excellent instrument for hedging health shock risk and for consumption smoothing across different health states. Optimal critical illness insurance demand is decreasing in financial wealth and increasing in human wealth. Real estate prices have a minor influence on optimal critical illness insurance demand.     

基于混合跳扩散模型的最优投资消费和寿险购买策略研究

本文研究在混合跳扩散模型下投资者分别投资于寿险、零息债券和股票时,关于最优投资消费和寿险购买的随机策略问题。通过构造满足混合跳扩散模型的金融市场、保险市场和可容许策略,在CRRA(constant relative risk aversion)效用下,利用动态规划的方法求解了对应的HJB方程,获得了值函数和最优策略的显式表达式。为了探索模型的有效性,本文给出了相对风险厌恶系数的数值分析以及相关参数对最优策略的影响。