Optimal investment and consumption with unknown parameters

An investment and consumption problem is formulated and its optimal strategy is investigated. We assume the basic binary model, but with unknown parameters. We apply the parametric Bayesian approach to formulate the problem as a sequential stochastic optimization model and use the technique of dynamic programming to characterize the optimal strategy. It is discovered that despite unknown parameters, when the power and logarithmic utility functions are treated, the optimal value function is of the same form of the utility function. The random finite horizon model is formulated as an infinite horizon model. Our results are similar to the ones in the literature having different return functions with constant relative risk aversion.     

Optimal asset allocation for participating contracts with mortality risk under minimum guarantee

Abstract

We investigate an optimal investment problem of participating insurance contracts with mortality risk under minimum guarantee. The insurer aims to maximize the expected utility of the terminal payoff. Due to its piecewise payoff structure, this optimization problem is a non-concave utility maximization problem. We adopt a concavification technique and a Lagrange dual method to solve the problem and derive the representations of the optimal wealth process and trading strategies. We also carry out some numerical analysis to show how the portfolio insurance constraint impacts the optimal terminal wealth.     

基于持久收入和财富目标的跨时消费选择——中国城市居民消费行为的实证研究

 摘　　要:标准生命周期消费理论假定消费者有能力求解复杂的动态优化问题，这一假定至少在中国是不能成立的。本文从中国实际出发，提出了关于中国城市居民消费行为的基本假设。即由于存在信贷约束和消费支出高峰，中国城市居民跨时消费的理性选择是：在避免未来发生流动性约束的前提下尽可能平滑各个时期的消费。与之相对应，本文假定中国城市居民跨时消费决策的主要依据是财富目标和持久收入，并在此基础上构建了经济计量模型。实证分析的主要结论是：（1）1990年以来，随着城市居民财富目标的不断提高，持久收入的边际消费倾向呈持续下降趋势。（2）中国城市居民的消费行为的确存在一个学习和适应过程。     

James-stein estimation with constraints on the norm

Consider the problem of estimating a multivariate mean 0(pxl), p>3, based on a sample x^ ..., xn with quadratic loss function. We find an optimal decision rule within the class of James-Stein type decision rules when the underlying distribution is that of a variance mixture of normals and when the norm ||0|| is known. When the norm is restricted to a known interval, typically no optimal James-Stein type rule exists but we characterize a minimal complete class within the class of James-Stein type decision rules. We also characterize the subclass of James-Stein type decision rules that dominate the sample mean.     

Optimal investment-consumption and life insurance with capital constraints

Abstract

The aim of this paper is to solve an optimal investment, consumption and life insurance problem when the investor is restricted to capital guarantee. We consider an incomplete market described by a jump-diffusion model with stochastic volatility. Using the martingale approach, we prove the existence of the optimal strategy and the optimal martingale measure and we obtain the explicit solutions for the power utility functions.     

基于财富目标的居民储蓄行为

内容提要：本文在借鉴缓冲储备理论的基础上,结合中国实际提出了关于城镇居民储蓄行为的假设：即中国城镇居民同样也有财富目标,当实际财富低于该目标时,预防性储蓄动机就会占据主导地位,消费者将减少消费、增加储蓄。与缓冲储备理论的最大不同是,本文假定财富目标与持久收入的比率不是一个固定的值,当预期支出比预期收入增长的更快时,为了避免未来可能发生的流动性约束,消费者就不得不提高储蓄率。利用我国1999-2005年28个省的数据得到的估计结果表明,中国城镇居民的高储蓄现象可以从三个方面解释：一是就业率下降加大了居民收入的不确定性;二是教育、医疗价格上涨过快以至于许多家庭的预期支出增长率超过了预期收入的增长速度,三是收入差距扩大抑制了中、低收入家庭的消费需求。本文的另外一个重要发现是,近年来发展迅速的消费信贷对储蓄率的影响并不显著。     

Forecasting electricity consumption with extra-model information provided by consumers

SUMMARY Univariate time series models make efficient use of available historical records of electricity consumption for short-term forecasting. However, the information (expectations) provided by electricity consumers in an energy-saving survey, even though qualitative, was considered to be particularly important, because the consumers' perception of the future may take into account the changing economic conditions. Our approach to forecasting electricity consumption combines historical data with expectations of the consumers in an optimal manner, using the technique of restricted forecasts. The same technique can be applied in some other forecasting situations in which additional information-besides the historical record of a variable-is available in the form of expectations.     

Optimal Strategies for a Long-Term Static Investor

The optimal strategies for a long-term static investor are studied. Given a portfolio of a stock and a bond, we derive the optimal allocation of the capitals to maximize the expected long-term growth rate of a utility function of the wealth. When the bond has a constant interest rate, three models for the underlying stock price processes are studied: Heston model, 3/2 model, and jump diffusion model. We also study the optimal strategies for a portfolio in which the stock price process follows a Black-Scholes model and the bond process has a Vasicek interest rate that is correlated to the stock price.     

基于目标导向的银行理财产品最优费率研究

建立基于银行目标导向的理财产品费率模型,通过对不同目标下银行行为的讨论,得出理财产品费率调整的一个分析框架。研究发现：存在使银行的经济效益和社会效益综合提升程度最大的最优理财产品费率;最优费率不是固定值,而是一个动态概念;单纯考虑经济效益时,银行将调高理财产品费率;银行调高理财产品费率,将提升自身综合目标的实现程度;银行调低理财产品费率,并不改变银行的综合目标。     

Cointegration and Long-Run Asset Allocation

We show that economic restrictions of cointegration between asset cash flows and aggregate consumption have important implications for return dynamics and optimal portfolio rules, particularly at long investment horizons. When cash flows and consumption share a common stochastic trend (i.e., are cointegrated), temporary deviations between their levels forecast long-horizon dividend growth rates and returns, and consequently, alter the term profile of risks and expected returns. We show that the optimal asset allocation based on the error-correction vector autoregression (EC-VAR) specification can be quite different relative to a traditional VAR that ignores the cointegrating relation. Unlike the EC-VAR, the commonly used VAR approach to model expected returns focuses on short-run forecasts and can considerably miss on long-horizon return dynamics, and hence, the optimal portfolio mix in the presence of cointegration. We develop and implement methods to account for parameter uncertainty in the EC-VAR setup and highlight the importance of the error-correction channel for optimal portfolio decisions at various investment horizons.     

Economic-demographic results of the life of one cohort (based on the cohort born in 1950)

Data from a five percent sample of the Soviet population, collected in 1985, are used to analyze the demographic and economic characteristics of the cohort born in 1950. Factors considered include mortality, marriage and divorce, income, consumption, and wealth. Differences in these factors by age and region are explored.     

Bayesian variable selection with strong heredity constraints

In this paper, we propose a Bayesian variable selection method for linear regression models with high-order interactions. Our method automatically enforces the heredity constraint, that is, a higher order interaction term can exist in the model only if both of its parent terms are in the model. Based on the stochastic search variable selection George and McCulloch (1993), we propose a novel hierarchical prior that fully considers the heredity constraint and controls the degree of sparsity simultaneously. We develop a Markov chain Monte Carlo (MCMC) algorithm to explore the model space efficiently while accounting for the heredity constraint by modifying the shotgun stochastic search algorithm Hans et al. (2007). The performance of the new model is demonstrated through comparisons with other methods. Numerical studies on both real data analysis and simulations show that our new method tends to find relevant variable more effectively when higher order interaction terms are considered.     

养老保险可携带性、农村劳动力流动与农村反贫困

本文在三部门经济框架下拓展了Harris和Todaro(1970)关于劳动力流动及其经济与社会影响的H-T模型,对养老保险可携带性影响农村劳动力流动的收入增长效应和贫富调节机制开展了理论及实证研究。结果显示:经济发展水平和产业层级在地区之间的梯度分化与城乡之间高达1.9~2.6倍的收入差距,是农村劳动力向城镇流动以及在不同城镇之间跨区流动的根本原因。养老保险可携带性是通过改变流动成本和流动收益影响农村劳动力的流动效率和流动方向,具有显著的收入增长效应和贫富调节作用。提高养老保险可携带性在2000—2019年间可使农村劳动力收入提高 35%以上,并可使城乡劳动 力收入差距减少15%~34%。有力地验证了《城镇企业职工基本养老保险关系转移接续暂行办法》在城乡协同发展、增加农民收入和缩小城乡贫富差距中的积极作用及其进一步完善的必要性和方向。     

Minimum bias designs with constraints

A new class of model-robust optimality criteria, based on the mean squared error, is introduced in this paper. The motivation is to find designs when the researcher is more concerned with controlling the variance than the bias, or vice versa. The set of criteria proposed here is also appealing from a mathematical perspective in the sense that, unlike the Box and Draper (1959, J. Amer. Statist. Assoc. 54, 622–654), criterion, they can be imbedded in the framework of convex design theory and, hence, facilitate the search for globally optimal designs. The basic idea is to minimize a convex function of the bias part of the mean squared error subject to a convex constraint on the variance part, or vice versa. Equivalence theorems are derived and examples for the linear and quadratic regression problems are provided.     

财政支农、农村居民消费与农民增收的动态分析——以辽宁省为例

政府财政支出和居民消费的关系一直是经济界争论的焦点,文章基于1980-2007年辽宁省的时间序列数据,从宏观和动态的角度,运用单位根检验,Granger因果检验和向量自回归模型考察辽宁省财政支农,农村居民消费以及收入之间的关系,向量自回归模型的动态分析表明：农村居民收入和消费之间具有相互促进的正向联系,而财政支出的各方面对居民收入和消费的影响不尽相同,其中,基本建设支出对居民消费和收入都有负影响．即产生“挤出效应”,而生产性支出对居民收入产生正影响,而对居民消费却产生“挤出效应”,科技项目支出对居民收入和消费,先产生负影响,随着时间的推移,影响变为正;其他财政支出对居民收入产生正的影响,而对居民消费先产生“挤出效应”,随后又促进居民消费。     

Optimal allocation of stratified samples with several variance constraints and equal workloads over time by geometric programming

We apply geometric programming, developed by Duffin, Peterson and Zener (1967), to the optimal allocation of stratified samples with several variance constraints arising from several estimates of deficiency rates in the quality control of administrative decisions. We develop also a method for imposing constraints on sample sizes to equalize workloads over time, as required by the practicalities of clerical work for quality control.

We allocate samples by an extension of the work of Neyman (1934), following the exposition of Cochran (1977). Davis and Schwartz (1987) developed methods for multiconstraint Neyman allocation by geometric programming for integrated sampling. They also applied geometric programming to Neyman allocation of a sample for estimating college enrollments by Cornell (1947) and Cochran (1977). This paper continues the application of geometric programming to Neyman allocation with multiple constraints on variances and workloads and minimpal sampling costs.     

Assessing local influence for elliptical linear models under equality constraints

ABSTRACT

In this article, we study the local influence for the elliptical linear regression model under equality constraints. We first obtain the parameter estimators of this model using the penalized log-likelihood function and iterative techniques. Then we obtain the diagnostics under the perturbations of constant variance, responses, and explanatory variables in the spirit of Cook (1986 Cook, R.D. (1986). Assessment of local influence. J. Royal Stat. Soc. Ser. B 48(2):133–169. [Google Scholar]). Finally, a numerical example on the data set of the salinity of water is given to illustrate the theoretical results.     

Dynamic optimal capital growth of diversified investment

We investigate the problem of dynamic optimal capital growth of diversified investment. A general framework that the trader maximize the expected log utility of long-term growth rate of initial wealth was developed. We show that the trader's fortune will exceed any fixed bound when the fraction is chosen less than critical value. But, if the fraction is larger than that value, ruin is almost sure. In order to maximize wealth, we should choose the optimal fraction at each trade. Empirical results with real financial data show the feasible allocation. The larger the fraction and hence the larger the chance of falling below the desired wealth growth path.     

Combining forecast quantiles using quantile regression: Investigating the derived weights, estimator bias and imposing constraints

SUMMARY A novel proposal for combining forecast distributions is to use quantile regression to combine quantile estimates. We consider the usefulness of the resultant linear combining weights. If the quantile estimates are unbiased, then there is strong intuitive appeal for omitting the constant and constraining the weights to sum to unity in the quantile regression. However, we show that suppressing the constant renders one of the main attractive features of quantile regression invalid. We establish necessary and sufficient conditions for unbiasedness of a quantile estimate, and show that a combination with zero constant and weights that sum to unity is not necessarily unbiased.     

Stock Returns and Expected Business Conditions: Half a Century of Direct Evidence

Using survey data, we characterize directly the impact of expected business conditions on expected excess stock returns. Expected business conditions consistently affect expected excess returns in a counter-cyclical fashion. Moreover, inclusion of expected business conditions in otherwise-standard predictive return regressions substantially reduce the explanatory power of the conventional financial predictors, including the dividend yield, default premium, and term premium, while simultaneously increasing R². Expected business conditions retain predictive power even when including the key nonfinancial predictor, the generalized consumption/wealth ratio. We argue that time-varying expected business conditions likely capture time-varying risk, whereas time-varying consumption/wealth may capture time-varying risk aversion.