随机金融市场环境下的最优再保险–投资策略

为了对冲保险风险,保险公司可以向再保险公司购买比例再保险;同时,为了保值增值,保险公司将其财富投资于金融市场.假设盈余过程由带漂移的布朗运动所驱动,利率满足仿射利率模型,股票波动率满足Heston随机波动率模型.应用随机最优控制和HJB方程方法得到了指数效用下最优再保险–投资策略的显式解.给出数值算例并分析了模型参数对最优再保险策略和最优投资策略的影响.研究结果表明:最优再保险策略不仅依赖于保险市场参数,而且依赖于金融市场参数;随机利率与随机波动率模型下的最优再保险–投资策略与利率动态密切相关,而与波动率动态无关;再保险行为对投资于股票的数量没有影响,而对投资于零息票债券的数量产生较大的影响.     

Heston模型中具有保费退回的确定缴费型养老金均衡投资策略

本文基于均方差准则研究了Heston模型中确定缴费型养老金(defined contribution,DC)计划的最优投资策略.假定养老金计划可投资于一种无风险资产和一种风险资产(股票),风险资产的价格服从收益率和波动率均为随机的Heston模型.此外,为了保护在基金积累阶段意外死亡的投保人的利益,假定保费可退回(给其继承人).本文在博弈论框架下给出了相应的HJB方程系统,并通过求解相应的HJB方程系统,得到了最优"时间一致"均衡投资策略以及均衡有效前沿的解析式.据我们所知,这是首次在具有保费退回的情形中研究Heston模型中DC计划的均方差均衡投资问题.文章最后分析了最优均衡投资策略和有效前沿的相关性质.     

具有异常波动市场的消费与投资策略

讨论了异常波动市场中容许借贷的消费与投资策略问题,阐述了随机最优控制理论应用于现代金融理论研究中的一种方法.首先给出了金融市场中不确定性的随机模型,利用It^o公式,得到了与消费及投资策略有关的财富过程的随机微分方程,并建立了最优消费与投资问题的随机控制模型.根据随机最优控制理论,导出了目标函数满足的Hamilton-Jacobi-Bellman(HJB)方程.通过对HJB方程的讨论,得到了最优消费与投资策略的分段表示函数,并就Hara效用函数进行讨论,得到了具体的消费与投资策略.     

均值回复收益的消费效用无差别定价

假设项目收益服从算术均值回复过程, 运用消费效用无差别定价原理, 得出决策者在非完备市场下最优投资消费策略以及最优目标函数, 与完备市场中项目收益波动率增加引起投资触发水平单方面增加所不同的是, 在非完备市场情形下还须考虑决策者的风险规避动机对投资决策的影响, 讨论了这一影响在一次性回报与现金流回报两种情形下的不同表现, 给出了相应解释, 指出了项目收益的均值回复速度与投资触发水平之间的相互变动关系.     

效用理论在信息安全投资优化中的应用

为了解决组织预算过程中信息安全投资最优的问题,建立了安全投资与风险控制的关系模型,对安全投资的有效性进行了研究,提出了降低事件发生概率有效性及缓解损失有效性的新概念.采用效用理论作为组织财富、风险损失和安全投资的描述模型,指数效用函数作为组织投资收益的描述模型.分析了安全投资的边界,使用求偏导数取极值的方法对投资效用函数进行了研究,并求得最小投资的解.应用实例表明,基于效用的风险度量方法是科学的,损失效应越大的安全事件需要更大的安全投资.     

存贷利率不等下具有随机跳跃收入的消费与投资策略

研究贷款利率大于存款利率下具有随机跳跃收入的最优策略,拓展了Merton模型.给出了财富预算方程,运用动态规划原理及随机分析导出该问题的HJB方程,并由此得到一般情形下抽象形式的解.在一类特殊HARA情形下讨论了具有显式反馈形式的最优消费和投资策略.     

基于后悔理论的灰色随机多准则决策方法

针对准则值和状态概率均为区间灰数的灰色随机多准则决策问题,在考虑决策者的风险态度及心理行为的情境下,给出一种基于后悔理论的决策方法.首先将原始准则值转化为标准灰数, 同时进行规范化处理, 得到各状态下的标准灰色风险决策矩阵;然后依据后悔理论,定义灰色感知效用函数,构造决策者对方案集的灰色综合感知效用最大化的多目标优化模型,并解出最优权重向量,得到各方案的最优灰色感知效用值且排序;最后,通过实例验证所提出方法的可行性和有效性.     

一个风险敏感最优控制问题的随机最大值原理及在投资选择中的应用

在本文, 我们主要研究了一类产生于金融市场中投资选择问题的风险敏感最优控制问题. 用经典的凸变分技术, 我们得到了该类问题的最大值原理. 最大值原理的形式相似于风险中性的情形. 但是, 对偶方程和变分不等式明显地依赖于风险敏感参数 γ. 这是与风险中性情形的主要区别之一. 我们用该结果解决一类最优投资选择问题. 在投资者仅投资国内债券和股票的情况下, 前人用贝尔曼动态规划原理所得的最优投资策略仅是我们结果的特殊形式. 我们也给了一些数值算例和图, 他们显式地解释了最大期望效用和模型中参数的关系.     

随机波动环境下库存管理研究

考虑一需求为复合Poisson分布、提前期为指数分布和短缺损失的连续检查库存系统,在假设供应商的状态和需求到达率均受到独立的随机波动环境影响下,利用水平穿越法,确定了零售商库存水平的平稳分布函数.在此基础上,构建了服务水平约束条件下长程平均总费用率最小化模型,并利用交叉熵法得到最优(r,Q)库存控制策略.最后,通过仿真实验分析了环境变化对最优库存和平均费用率的影响.     

多阶段均值–方差资产负债管理的随机控制

资产负债管理研究如何合理分配资产以到达最小化风险同时确保期望剩余财富(财富减去负债)达到一定水平.本文在均值–方差投资组合理论的框架下研究两类资产负债管理模型, 包括带有跨期均值–方差投资目标和带有非破产约束的模型. 由于在动态规划意义下, 方差不具有可分性质, 传统的随机最优控制方法难以直接应用. 如采用处理动态均值–方差优化问题的嵌入法来解决以上问题会带来计算上的困难. 本文借鉴平均场控制的思想对以上两类问题加以研究. 本文假设了非常宽泛的市场模型: 所有的资产都是风险资产; 债务和风险资产之间存在相关性. 在此市场假设模型下, 本文给出了最优投资策略(控制率)的解析表达式和均值–方差有效前沿的表达形式. 本研究成果为投资者提供了新的投资策略, 可应用于更复杂的资产负债管理中.     

Portfolio optimization with Markov-modulated stock prices and interest rates

A financial market with one bond and one stock is considered where the risk free interest rate, the appreciation rate of the stock and the volatility of the stock depend on an external finite state Markov chain. We investigate the problem of maximizing the expected utility from terminal wealth and solve it by stochastic control methods for different utility functions. Due to explicit solutions it is possible to compare the value function of the problem to one where we have constant (average) market data. The case of benchmark optimization is also considered.     

Mean–variance portfolio selection based on a generalized BNS stochastic volatility model

We study a mean–variance portfolio selection problem via optimal feedback control based on a generalized Barndorff-Nielsen and Shephard stochastic volatility model, where an investor trades in a generalized Black–Scholes market. The random coefficients of the market are driven by non-Gaussian Ornstein–Uhlenbeck processes that are independent of the underlying multi-dimensional Brownian motion. Our contribution is to explicitly compute and justify optimal portfolios over an admissible set that is large enough to cover some important classes of strategies such as the class of feedback controls of Markov type. Concretely, the mean–variance efficient portfolios and efficient frontiers are explicitly calculated through the method of generalized linear-quadratic control and explicitly constructed solutions to three integro-partial differential equations under a quite mild condition that only requires one stock whose appreciation-rate process is different from the interest-rate process. Related minimum variance issue is also addressed via our main results.     

Forecasting the volatility of stock price index

Accurate volatility forecasting is the core task in the risk management in which various portfolios’ pricing, hedging, and option strategies are exercised. Prior studies on stock market have primarily focused on estimation of stock price index by using financial time series models and data mining techniques. This paper proposes hybrid models with neural network and time series models for forecasting the volatility of stock price index in two view points: deviation and direction. It demonstrates the utility of the hybrid model for volatility forecasting. This model demonstrates the utility of the neural network forecasting combined with time series analysis for the financial goods.     

Estimating stochastic volatility models using daily returns and realized volatility simultaneously

Realized volatility, which is the sum of squared intraday returns over a certain interval such as a day, has recently attracted the attention of financial economists and econometricians as an accurate measure of the true volatility. In the real market, however, the presence of non-trading hours and market microstructure noise in transaction prices may cause bias in the realized volatility. On the other hand, daily returns are less subject to noise and therefore may provide additional information on the true volatility. From this point of view, modeling realized volatility and daily returns simultaneously based on the well-known stochastic volatility model is proposed. Empirical studies using intraday data of Tokyo stock price index show that this model can estimate realized volatility biases and parameters simultaneously. The Bayesian approach is taken and an efficient sampling algorithm is proposed to implement the Markov chain Monte Carlo method for our simultaneous model. The result of the model comparison between the simultaneous models using both naive and scaled realized volatilities indicates that the effect of non-trading hours is more essential than that of microstructure noise and that asymmetry is crucial in stochastic volatility models. The proposed Bayesian approach provides an estimate of the entire conditional predictive distribution of returns under consideration of the uncertainty in the estimation of both biases and parameters. Hence common risk measures, such as value-at-risk and expected shortfall, can be easily estimated.     

Funding and investment decisions in a stochastic defined benefit pension plan with several levels of labor-income earnings

In this paper we consider the optimal management of an aggregated dynamic pension fund. There are n$n$ classes of workers whose salaries are stochastic. A portion of the salary is contributed to the funding process and the manager invests in a portfolio with m$m$ risky assets and a risk-free security. The main objective is to minimize the cost of contributions in a bounded horizon T$T$ and to maximize the utility of final surplus, measured as the relative fund level respect to the mean salary. The aim of the paper is to describe the properties of fund allocation and optimal contribution when salaries differ across contributors to the fund.     

A multivariate threshold stochastic volatility model

We introduce in this paper a multivariate threshold stochastic volatility model for multiple financial return time series. This model allows the dynamic structure of return and volatility to change according to a threshold model while accounting for the interdependence of financial returns. Through the threshold volatility modeling, we can understand the impact of market news on volatility asymmetry. Estimation of unknown parameters are carried out using Markov chain Monte Carlo techniques. Simulations show that our estimators are reliable in moderately large sample sizes. We apply the model to three market indice data and estimate time-varying correlations among the indice returns.     

Modelling and asset allocation for financial markets based on a stochastic volatility microstructure model

On the basis of the market microstructure theory, a continuous time microstructure model is proposed for describing the dynamics of financial markets with stochastic volatility property. From the microstructure model, one may obtain the estimates of two state variables, which represent the market excess demand and liquidity respectively but cannot be directly observed. Based on the indirectly obtained excess demand information instead of the prediction of price, a simple asset dynamic allocation approach is investigated. The local linearization method, nonlinear Kalman filter and maximum likelihood method-based estimation approach for the microstructure model proposed is presented. Case studies on the financial markets modelling and the estimated model-based asset dynamic allocation control for the JPY/USD (Japanese Yen/US Dollar) exchange rate and Japan TOPIX (Tokyo stock Price IndeX) show a satisfactory modelling precision and dynamic allocation performance.     

A multiple objective stochastic portfolio selection problem with random Beta

When selecting a portfolio, we need to consider, in general, the portfolio return and portfolio risk. Many risk measures have been used in portfolio selection problems as the Beta risk measure, introduced by the capital asset pricing model. Most of the existing research papers suppose that security's Beta has a deterministic value. Recently, many researchers argued that in selecting the optimal portfolio, securities’ Beta should be considered as an uncertain parameter. In this paper, we set up fundamentals to model the portfolio's Beta as a random variable and propose a multiple objective stochastic portfolio selection model with random Beta. To solve the proposed model, we apply a stochastic goal programming approach. A numerical example from the US stock exchange market is reported.     

A New Predictive Measure Using Agent-Based Behavioral Finance

We calibrate Friedman and Abraham’s (J Econ Dyn Control 33:922–937, 2009) agent-based model using actual financial data in the US stock market. The evidence shows that the estimated price series from the model is similar to real S&P price series and the model does match return moments at the second and higher order. In addition, we develop a new measure of investor heterogeneity based on the variability in the estimated position sizes across all mutual fund managers. Our results show that the volatility in individual fund manager positions is able to predict future returns in various time horizons. Moreover, increased variability in position sizes positively affects the contemporaneous change in the CBOE Volatility Index and also leads to greater probability of recession.     

Forecasting the volatility of a combined multi‐country stock index using GWMA algorithms

Globalization has increased the volatility of international financial transactions, particularly those related to international stock markets. An increase in the volatility of one country's stock market spreads throughout the globe, affecting other countries' stock markets. In particular, the Dow Jones Industrial Average plays an extremely important role in the international stock market. This paper uses the generally weighted moving average method and data from the Dow Jones Industrial Average, the National Association of Securities Dealers Automated Quotations, Japan's Nikkei 225, the Korea Composite Stock Price Index, and the Hong Kong Hang Seng Index to predict the performance of the Taiwan Capitalization Weighted Stock Index. This paper attempts to find the smallest prediction error using the optimal combination of generally weighted moving average model parameters and combinations of various international stock market data and compares the results to that found using the exponentially weighted moving average model to explore differences between the two types of forecasting models.