Time-varying parameter auto-regressive models for autocovariance nonstationary time series

In this paper, autocovariance nonstationary time series is clearly defined on a family of time series. We propose three types of TVPAR (time-varying parameter auto-regressive) models: the full order TVPAR model, the time-unvarying order TVPAR model and the time-varying order TVPAR model for autocovariance nonstationary time series. Related minimum AIC (Akaike information criterion) estimations are carried out. This work was supported by the Doctoral Research Fund of the Ministry of Education, China (Grant No. 20040285008), and Grant-in-Aid for Scientific Research (B), the Ministry of Education, Science, Sports and Culture, Japan, 2005 (Grant No. 17300228)     

A class of portfolio selection with a four-factor futures price model

Considering the stochastic exchange rate, a four-factor futures model with the underling asset, convenience yield, instantaneous risk free interest rate and exchange rate, is established. These processes follow jump-diffusion processes (Weiner process and Poisson process). The corresponding partial differential equation (PDE) of the futures price is derived. The general solution of the PDE with parameters is drawn. The weight least squares approach is applied to obtain the parameters of above PDE. Variance is substituted by semi-variance in Markowitzs portfolio selection model. Therefore, a class of multi-period semi-variance model is formulated originally. Then, a continuous-time mean-variance portfolio model is also considered. The corresponding stochastic Hamilton-Jacobi-Bellman (HJB) equation of the problem with nonlinear constraints is derived. A numerical algorithm is proposed for finding the optimal solution in this paper. Finally, in order to demonstrate the effectiveness of the theoretical models and numerical methods, the fuel futures in Shanghai exchange market and the Brent crude oil futures in London exchange market are selected to be examples.     

A possibilistic mean-semivariance-entropy model for multi-period portfolio selection with transaction costs

This paper deals with a multi-period portfolio selection problem with fuzzy returns. A possibilistic mean-semivariance-entropy model for multi-period portfolio selection is presented by taking into account four criteria viz., return, risk, transaction cost and diversification degree of portfolio. In the proposed model, the return level is quantified by the possibilistic mean value of return, the risk level is characterized by the lower possibilistic semivariance of return, and the diversification degree of portfolio is measured by the originally presented possibilistic entropy. Furthermore, a hybrid intelligent algorithm is designed to obtain the optimal portfolio strategy. Finally, the comparison analysis between the possibilistic entropy model and the proportion entropy model is provided by two numerical examples to illustrate the efficiency of the proposed approaches and the designed algorithm.     

Mean-semivariance models for fuzzy portfolio selection

This paper discusses portfolio selection problem in fuzzy environment. In the paper, semivariance is originally presented for fuzzy variable, and three properties of the semivariance are proven. Based on the concept of semivariance of fuzzy variable, two fuzzy mean-semivariance models are proposed. To solve the new models in general cases, a fuzzy simulation based genetic algorithm is presented in the paper. In addition, two numerical examples are also presented to illustrate the modelling idea and the effectiveness of the designed algorithm.     

Neural networks and flexible approximations

Email: cuny{at}cardiff.ac.uk This paper supports the view that neural networks are best seenas devices that can approximate a wide range of functions. Theauthors argue the need to consider the precise details of howthe approximations operate in practice. The paper shows howstandard network models can be regarded as polynomial functions,obtained from expanding exponential terms. Multivariate Taylor-seriesexpansions, obtained through the MAPLE software package, areused for this purpose. The expansions serve to cast light onthe role of the hidden nodes. Also considered is the relativedifficulty of fitting different types of function. Quadraticfunctions are compared with Gaussian shapes.     

Distribution assumptions and risk constraints in portfolio optimization

Empirical distributions are often claimed to be superior to parametric distributions, yet to also increase the computational complexity and are therefore hard to apply in portfolio optimization. In this paper, we approach the portfolio optimization problem under constraints on the portfolios Value at Risk and Expected Tail Loss, respectively, under empirical distributions for the Standard and Poors 100 stocks. We apply a heuristic optimization method which has been found to overcome the restrictions of traditional optimization techniques. Our results indicate that empirical distributions might turn into a Pandoras Box: Though highly reliable for predicting the assets risks, employing these distributions in the optimization process might result in severe mis-estimations of the resulting portfolios actual risk. It is found that even a simple mean-variance approach can be superior despite its known specification errors.AMS Classification: G11, C61Dietmar G. Maringer: Im grateful to two anonymous referees, Peter Winker, Manfred Gilli, Berç Rustem, Erricos Kontoghiorghes, Alfred Lehar, Josef Zechner, Suresh Sundaresan, and conference participants at Aix-en-Provence, Limassol, and Sydney for valuable discussions and comments on earlier versions of this paper.     

Numerical approximations of chromatographic models

A numerical scheme based on modified method of characteristics with adjusted advection (MMOCAA) is proposed to approximate the solution of the system liquid chromatography with multi components case. For the case of one component, the method preserves the mass. Various examples and computational tests numerically verify the accuracy and efficiency of the approach.     

Concentrated portfolio selection models based on historical data

A new risk measure fully based on historical data is proposed, from which we can naturally derive concentrated optimal portfolios rather than imposing cardinality constraints. The new risk measure can be expressed as a quadratics of the introduced greedy matrix, which takes investors' joint behavior into account. We construct distribution‐free portfolio selection models in simple case and realistic case, respectively. The latest techniques for describing transaction cost constraints and solving nonconvex quadratic programs are utilized to obtain the optimal portfolio efficiently. In order to show the practicality, efficiency, and robustness of our new risk measure and corresponding portfolio selection models, a series of empirical studies are carried out with trading data from advanced stock markets and emerging stock markets. Different performance indicators are adopted to comprehensively compare results obtained under our new models with those obtained under the mean‐variance, mean‐semivariance, and mean‐conditional value‐at‐risk models. Out‐of‐sample results sufficiently show that our models outperform the others and provide a simple and practical approach for choosing concentrated, efficient, and robust portfolios. Copyright © 2014 John Wiley & Sons, Ltd.     

Adaptive control of three continuous-time portfolio and consumption models

An economic application of adaptive control is presented using three continuous time portfolio and consumption models that are natural generalizations of a model of Merton. In these models of the wealth of an individual investor, it is assumed that the various parameters are deterministic functions of time or stochastic processes. An adaptive control problem arises for each of these models when it is assumed that the average return rate of the risky asset, which is either a deterministic function or a stochastic process, is not observed. For these models, a recursive family of estimators of the average return rate of the risky asset is given based on the observations of the wealth. These estimates are used in the control of the wealth equation.This research was partially supported by NSF Grant No. ECS-84-03286-A01 and by University of Kansas General Research Allocation No. 3806-XO-0038.     

Credit risk optimization using factor models

We study portfolio credit risk management using factor models, with a focus on optimal portfolio selection based on the tradeoff of expected return and credit risk. We begin with a discussion of factor models and their known analytic properties, paying particular attention to the asymptotic limit of a large, finely grained portfolio. We recall prior results on the convergence of risk measures in this “large portfolio approximation” which are important for credit risk optimization. We then show how the results on the large portfolio approximation can be used to reduce significantly the computational effort required for credit risk optimization. For example, when determining the fraction of capital to be assigned to particular ratings classes, it is sufficient to solve the optimization problem for the large portfolio approximation, rather than for the actual portfolio. This dramatically reduces the dimensionality of the problem, and the amount of computation required for its solution. Numerical results illustrating the application of this principle are also presented. JEL Classification G11     

Convergence of coercive approximations for strictly monotone quasistatic models in inelastic deformation theory

This article studies coercive approximation procedures in the infinitesimal inelastic deformation theory. For quasistatic, strictly monotone, viscoplastic models using the energy method and the Young measures approach a convergence theorem in generalized Orlicz spaces is proved. The main step in the proof is a characterization of the weak limit of non‐linear terms by the convergence in measure. Copyright © 2007 John Wiley & Sons, Ltd.     

Baseline value specification and sensitivity analysis in multiattribute project portfolio selection

A key issue in applying multi-attribute project portfolio models is specifying the baseline value – a parameter which defines how valuable not implementing a project is relative to the range of possible project values. In this paper we present novel baseline value specification techniques which admit incomplete preference statements and, unlike existing techniques, make it possible to model problems where the decision maker would prefer to implement a project with the least preferred performance level in each attribute. Furthermore, we develop computational methods for identifying the optimal portfolios and the value-to-cost -based project rankings for all baseline values. We also show how these results can be used to (i) analyze how sensitive project and portfolio decision recommendations are to variations in the baseline value and (ii) provide project decision recommendations in a situation where only incomplete information about the baseline value is available.     

The optimal solution of ESG portfolio selection models that are based on the average ESG score

Recently, various models have been proposed to engage portfolio selection or ESG investments. In this brief report, we solve the problem of optimal portfolio selection of arbitrary ESG utility functions where the ESG preference function is based on the average ESG score. The proposed optimal solution shows that the impact of the ESG score and the expected return vectors on the optimal weights are equal, up to a scalar, regardless of the utility function of the investors.     

Time-invariant portfolio strategies in structured products with guaranteed minimum equity exposure

We introduce a new exotic option to be used within structured products to address a key disadvantage of standard time-invariant portfolio protection: the well-known cash-lock risk. Our approach suggests enriching the framework by including a threshold in the allocation mechanism so that a guaranteed minimum equity exposure (GMEE) is ensured at any point in time. To be able to offer such a solution still with hard capital protection, we apply an option-based structure with a dynamic allocation logic as underlying. We provide an in-depth analysis of the prices of such new exotic options, assuming a Heston–Vasicek-type financial market model, and compare our results with other options used within structured products. Our approach represents an interesting alternative for investors aiming at downsizing protection via time-invariant portfolio protection strategies, meanwhile being also afraid to experience a cash-lock event triggered by market turmoils.     

Signed graphs for portfolio analysis in risk management

We introduce the notion of structural balance for signed graphsin the context of portfolio analysis. A portfolio of securitiescan be represented as a signed graph with the nodes denotingthe securities and the edges representing the correlation betweenthe securities. With signed graphs, the characteristics of aportfolio from a risk management perspective can be uncoveredfor analysis purposes. It is shown that a portfolio characterizedby a signed graph of positive and negative edges that is structurallybalanced is characteristically more predictable. Investors whoundertake a portfolio position with all positively correlatedsecurities do so with the intention to speculate on the upside(or downside). If the portfolio consists of negative edges andis balanced, then it is likely that the position has a hedgingdisposition within it. On the other hand, an unbalanced signedgraph is representative of an investment portfolio which ischaracteristically unpredictable.     

Asymptotic expansions for the Laplace approximations for Itô functionals of Brownian rough paths

In this paper, we establish asymptotic expansions for the Laplace approximations for Itô functionals of Brownian rough paths under the condition that the phase function has finitely many non-degenerate minima. Our main tool is the Banach space-valued rough path theory of T. Lyons. We use a large deviation principle and the stochastic Taylor expansion with respect to the topology of the space of geometric rough paths. This is a continuation of a series of papers by Inahama [Y. Inahama, Laplace's method for the laws of heat processes on loop spaces, J. Funct. Anal. 232 (2006) 148-194] and by Inahama and Kawabi [Y. Inahama, H. Kawabi, Large deviations for heat kernel measures on loop spaces via rough paths, J. London Math. Soc. 73 (3) (2006) 797-816], [Y. Inahama, H. Kawabi, On asymptotics of certain Banach space-valued Itô functionals of Brownian rough paths, in: Proceedings of the Abel Symposium 2005, Stochastic Analysis and Applications, A Symposium in Honor of Kiyosi Itô, Springer, Berlin, in press. Available at: http://www.abelprisen.no/no/abelprisen/deltagere_2005.html].     

A DIRECT METHOD IN OPTIMAL PORTFOLIO AND CONSUMPTION CHOICE

In this paper, we use a direct method to solve the optimal portfolio and consumption choice problem in the security market for a specific case, in which the utility function is of a given homogenous form, i.e. the so-called CRRA case. The idea comes from the completion technique ever used in LQ optimal control.     

Optimal decision rule in forming an insurance portfolio

The paper is devoted to finding an optimal decision rule for accepting/rejecting potential insureds when the demand for the insurance provision is a stochastic variable. A criterion to be maximized is the mean-variance utility function of the insurer. It is shown that the optimal decision rule is a stopping rule with some finite protection level.     

非平稳市场中适应性在线投资组合策略设计与分析

考虑到股票市场的表现往往是非平稳的, 过去较长时间的股票价格对当前的投资决策影响较小, 因此基于近期股票价格数据设计在线投资组合策略. 首先, 将上一期的策略与固定长度的股票价格近期数据对应的最优定常再调整策略加权平均, 设计了一个在线投资组合策略. 其次, 进一步采用在线学习的方法选择加权平均的权重, 设计了一个适应性的在线投资组合策略. 利用实际股票价格数据对构造的策略进行数值分析, 结果表明与基准策略和已有的在线投资组合策略相比, 设计的策略具有较好的性能.