Active allocation of systematic risk and control of risk sensitivity in portfolio optimization

Portfolio risk can be decomposed into two parts, the systematic risk and the nonsystematic risk. It is well known that the nonsystematic risk can be eliminated by diversification, while the systematic risk cannot. Thus, the portfolio risk, except for that of undiversified small portfolios, is always dominated by the systematic risk. In this paper, under the mean–variance framework, we propose a model for actively allocating the systematic risk in portfolio optimization, which can also be interpreted as a model of controlling risk sensitivity in portfolio selection. Although the resulting problem is, in general, a notorious non-convex quadratically constrained quadratic program, the problem formulation is of some special structures due to the features of the defined marginal systematic risk contribution and the way to model the systematic risk via a factor model. By exploiting such special problem characteristics, we design an efficient and globally convergent branch-and-bound solution algorithm, based on a second-order cone relaxation. While empirical study demonstrates that the proposed model is a preferred tool for active portfolio risk management, numerical experiments also show that the proposed solution method is more efficient when compared to the commercial software BARON.     

Insights to systematic risk and diversification across a joint probability distribution

This paper analyses and develops insights to systematic risk and diversification when random, imperfectly dependent, losses are aggregated. Systematic risk and diversification are shown to vary across layers of component losses according to local dependence and volatility structures. Systematic risk is high and diversification is weak overall if high risk layers are heavily dependent on the aggregate loss. This result explains weak diversification observed in financial markets despite weak to moderate correlations overall. A coherent risk setup is assumed in this paper, where risks are measured using distortion and allocated using the Euler principle.     

On the impact of infrequent trading on the APT systematic risk components — Evidence from a thin security market

The purpose of this note is to analyze the effects of infrequent trading on the APT systematic risk components using Finnish data. Infrequent trading is reported to influence especially the first systematic risk component produced by factor analysis on stock returns.     

Systematic mortality risk: An analysis of guaranteed lifetime withdrawal benefits in variable annuities

Guaranteed lifetime withdrawal benefits (GLWB) embedded in variable annuities have become an increasingly popular type of life annuity designed to cover systematic mortality risk while providing protection to policyholders from downside investment risk. This paper provides an extensive study of how different sets of financial and demographic parameters affect the fair guaranteed fee charged for a GLWB as well as the profit and loss distribution, using tractable equity and stochastic mortality models in a continuous time framework. We demonstrate the significance of parameter risk, model risk, as well as the systematic mortality risk component underlying the guarantee. We quantify how different levels of equity exposure chosen by the policyholder affect the exposure of the guarantee providers to systematic mortality risk. Finally, the effectiveness of a static hedge of systematic mortality risk is examined allowing for different levels of equity exposure.     

Statistical estimation for some dividend problems under the compound Poisson risk model

In this paper, we consider some dividend problems in the classical compound Poisson risk model under a constant barrier dividend strategy. Suppose that the Poisson intensity for the claim number process and the distribution for the individual claim sizes are both unknown. We use the COS method to study the statistical estimation for the expected present value of dividend payments before ruin and the expected discounted penalty function. The convergence rates under large sample setting are derived. Some simulation results are also given to show effectiveness of the estimators under finite sample setting.     

Investment volatility: A critique of standard beta estimation and a simple way forward

Beta is a widely used quantity in investment analysis. We review the common interpretations that are applied to beta in finance and show that the standard method of estimation – least squares regression – is inconsistent with these interpretations.     

Criterion of semi-Markov dependent risk model

A rigorous definition of semi-Markov dependent risk model is given. This model is a generalization of the Markov dependent risk model. A criterion and necessary conditions of semi- Markov dependent risk model are obtained. The results clarify relations between elements among semi-Markov dependent risk model more clear and are applicable for Markov dependent risk model.     

An integrated model for earthquake risk and damage assessment

The primary objective of this paper was to develop an integrated model for earthquake risk and damage assessment. This model consists of three major submodules - the physical damage functions, the economic damage functions, and the institutional aspects related to risk mitigation policies and community preparedness. While the physical damage functions are related to earthquake risk prediction utilizing both probabilistic and deterministic approaches, the economic damage functions refer to the potential vulnerability of various populations at earthquake risk.The feasibility of this model was tested with historical and projected data on earthquake risk and impacted populations for the New Madrid Fault region which includes St. Louis and Memphis Standard Metropolitan Statistical Areas. If the 1811–1812 New Madrid earthquakes would recur between 1980 and 2030, the damage results from the simulations of this model based on the status quo scenario, indicate that the region would experience structural losses in billions of dollars and a death toll of hundreds of persons.     

Decision making in stock trading: An application of PROMETHEE

The key issue for decision making in stock trading is selection of the right stock at the right time. In order to select the superior stocks (alternatives) for investment, a finite number of alternatives have to be ranked considering several and sometimes conflicting criteria. Therefore, we are faced with a special multicriteria decision-making problem. The purpose of this paper is to develop a decision-making model for selecting superior stocks in stock exchange and a model is provided in order to structure this problem. The proposed model is structured around two pillars: Industry evaluation and Company evaluation. The preference ranking organization method for enrichment evaluation (PROMETHEE) has been used for solving the problem. The model has been applied at Tehran Stock Exchange (TSE) as a real case and a survey from the experts in order to determine the effective criteria for industry evaluation and company evaluation has been conducted.     

Shortfall risk minimising strategies in the binomial model: characterisation and convergence

In this paper we study the dependence on the loss function of the strategy, which minimises the expected shortfall risk when dealing with a financial contingent claim in the particular situation of a binomial model. After having characterised the optimal strategies in the particular cases when the loss function is concave, linear or strictly convex, we analyse how optimal strategies change when we approximate a loss function with a sequence of suitable loss functions.The first author accomplished most of this research as a post-doc fellow in the Pure and Applied Mathematics Dept. of Padua University, which is gratefully acknowledged.     

粮食价格与居民消费价格关系的统计分析——1997.1—2005.4年粮价与物价的实证分析

通过对粮价与物价的格兰杰检验,给出粮价与物价就统计意义上的因果关系.并考虑到物价和粮价可能存在集群性,对粮价和物价建立误差修正-自回归条件异方差混合模型.     

Markov-modulated风险模型中盈余过程零点数的分布

基于保险公司在首次破产后仍能继续运转的情形,讨论并得到了Markovmodulated风险模型中盈余过程零点数的分布.     

一类相依索赔离散风险模型研究

研究了一类相依索赔的离散风险模型,得到了利率为0时模型的最终破产概率所满足的积分方程,以及破产持续n期的概率所满足的表达式.进而,得到了利率不为0时该模型的最终破产概率所满足的积分方程,并利用鞅论技巧导出了最终破产概率的一个Lundberg型上界,最后运用Matlab软件随机模拟破产概率并与Lundberg型上界作比较.     

The analysis and application of an HBV model

A mathematical model is formulated to describe the spread of hepatitis B. The stability of equilibria and persistence of disease are analyzed. The results shows that the dynamics of the model is completely determined by the basic reproductive number ρ₀. If ρ₀ < 1, the disease-free equilibrium is globally stable. When ρ₀ > 1, the disease-free equilibrium is unstable and the disease is uniformly persistent. Furthermore, under certain conditions, it is proved that the endemic equilibrium is globally attractive. Numerical simulations are conducted to demonstrate our theoretical results. The model is applied to HBV transmission in China. The parameter values of the model are estimated based on available HBV epidemic data in China. The simulation results matches the HBV epidemic data in China approximately.     

An asymptotic minimax risk bound for estimation of a linear functional relationship

We consider estimation of the parameter B in a multivariate linear functional relationship X_i=ξ_i+ξ_1i, Y_i=Bξ_i+ξ_2i, i=1,…,n, where the errors (ζ_1i^′, ζ_2i^′) are independent standard normal and (ξ_i, i ) is a sequence of unknown nonrandom vectors (incidental parameters). If there are no substantial a priori restrictions on the infinite sequence of incidental parameters then asymptotically the model is nonparametric but does not fit into common settings presupposing a parameter from a metric function space. A special result of the local asymptotic minimax type for the m.1.e. of B is proved. The accuracy of the normal approximation for the m.l.e. of order n^−1/2 is also established.     

Markov-modulated风险模型破产前最大盈余额与破产赤字的联合分布

应用逐段决定马尔可夫过程理论及补充变量技巧,使Markov-modulated风险过程成为齐次强马尔可夫过程,然后利用强马氏性及首达时间分布给出了其破产前最大盈余额与破产赤字的联合分布.     

Ruin problems for an autoregressive risk model with dependent rates of interest

In this paper, we consider a discrete insurance risk model in which the claims, the premiums and the rates of interest are assumed to have dependent autoregressive structures (AR(1)). We derive recursive and integral equations for expected discounted penalty function. By these equations, we obtain generalized Lundberg inequality for the infinite time severity of ruin and hence for the infinite time ruin probability, consider asymptotic formula for the finite time ruin probability when loss distributions have regularly varying tails, and study some probability properties of the duration of ruin.     

Replication and shortfall risk in a binomial model with transaction costs

The shortfall risk is defined as the optimal mean value of the terminal deficit produced by a self-financing portfolio whose initial value is smaller than what is required to replicate a contingent claim. In this paper we look for an explicit expression for it, as well as for the optimal strategy, when the market model is a binomial model with proportional transaction costs. We first study replication of European claims which satisfy suitable assumptions. We then investigate the shortfall minimization problem in a framework very similar to that without transaction costs. The author thanks the referee for useful comments on an earlier version of the present paper.     

A micro-movement model with Bayes estimation via filtering: Application to measuring trading noises and costs

We highlight a general hybrid system as the micromovement model for asset price using counting processes recently introduced with its Bayes estimation via filtering. We construct a new simple micromovement model and apply it to analyze trade-by-trade stock price data in the light of the series of works initiated by Christie and Schultz [Why do NASDAQ market makers avoid odd-eighth quotes?, Finance 49 (1994) 1813–1840]. Through the new model, we propose more reasonable, but computationally intensive measures for trading noise including clustering noise and non-clustering noise, and for trading cost. We employ Bayes estimation via filtering to obtain parameter estimates of the new model and to provide numerical measures of trading noise and trading cost for three stocks from four chosen periods. Our empirical results support the important findings in [Christie, Harris, Schultz, Why did NASDAQ market makers stop avoiding odd-eighth quotes?, Finance 49 (1994) 1841–1860; Barclay, Christie, Harris, Kandel, Schultz, The effects of market reform on the trading costs and depths of NASDAQ stocks, J. Finance 54(1) (1999) 1–34].