Optimal portfolio positioning within generalized Johnson distributions

Many empirical studies have shown that financial asset returns do not always exhibit Gaussian distributions, for example hedge fund returns. The introduction of the family of Johnson distributions allows a better fit to empirical financial data. Additionally, this class can be extended to a quite general family of distributions by considering all possible regular transformations of the standard Gaussian distribution. In this framework, we consider the portfolio optimal positioning problem, which has been first addressed by Brennan and Solanki [J. Financial Quant. Anal., 1981, 16, 279–300], Leland [J. Finance, 1980, 35, 581–594] and further developed by Carr and Madan [Quant. Finance, 2001, 1, 9–37] and Prigent [Generalized option based portfolio insurance. Working Paper, THEMA, University of Cergy-Pontoise, 2006]. As a by-product, we introduce the notion of Johnson stochastic processes. We determine and analyse the optimal portfolio for log return having Johnson distributions. The solution is characterized for arbitrary utility functions and illustrated in particular for a CRRA utility. Our findings show how the profiles of financial structured products must be selected when taking account of non Gaussian log-returns.     

Derivative pricing using multivariate affine generalized hyperbolic distributions

In this paper we use multivariate affine generalized hyperbolic (MAGH) distributions, introduced by Schmidt et al. (2006), to show how to price multidimensional derivatives when the underlying asset follows a MAGH distribution. We also illustrate the approach using market data from the BOVESPA (São Paulo Stock Exchange) and the exchange rate of the Brazilian Real vs. US Dollar to price some multidimensional derivatives.     

A fitting procedure for some generalized poisson distributions

Abstract

Many of the contagious distributions considered in the biological sciences are members of the generalized Poisson family. Four distributions which belong to this family and have been used frequently are the Negative Binomial (cf. Bliss [2]), Neyman Type A (cf. Beall and Rescia [1]), Poisson Binomial (cf. McGuire et al. [10]) and the generalized Polya-Aeppli (cf. Skellam [14]).     

Multivariate affine generalized hyperbolic distributions: An empirical investigation

The aim of this paper is to estimate multivariate affine generalized distributions (MAGH) using market data. We use the Ibovespa, CAC, DAX, FTSE, NIKKEI and S&P500 indexes. We estimate the univariate distributions, bi-variate distributions and six-dimensional distribution. Then we assess their goodness of fit using Kolmogorov distances. As an application we study the efficient frontier.     

Equilibrium preference free pricing of derivatives under the generalized beta distributions

This paper demonstrates that the risk neutral valuation relationship (RNVR) exists when the aggregate wealth and the underlying variable for derivatives follow a distribution from the family of transformed beta distributions. Specifically, the asset specific pricing kernel (ASPK) is solved for the generalized beta (GB) distribution class, which is extremely flexible to describe various shapes of underlying distributions. With the ASPK in hand, preference free call option formulas are obtained for rescaled and shifted beta distribution of the first kind (RSB1) and for the second kind (RSB2). These distributions include many well known important distributions as special cases. If the preference free formula does not exist under the GB distribution class, then the call price is shown to be numerically calculated without information of preference parameters once the spot price of the underlying is given.     

On evaluation of the Delaporte distribution and related distributions

Abstract

In the present paper we develop recursive algorithms for evaluation of the Delaporte distribution, the compound Delaporte distribution, and convolutions of compound Delaporte distributions. Some asymptotic results are given. We discuss how the approach can sometimes be generalized to other classes of compound mixed Poisson distributions when the mixing distribution is a shifted infinitely divisible distribution.     

Unbiased estimates of reliability for the truncated gamma distribution

Abstract

This paper derives the minimum variance unbiased estimate of the reliability function associated with the gamma distribution which is right truncated at a known point by using the classical minimum variance unbiased estimation method as outlined and initiated by Basu (1964). The techniques given are general and can be used to estimate not only the probability in the upper tail (reliability) of a distribution but also the probability content of any other region. In the sequel, the distribution of the minimal sufficient statistic, useful in inferential problems, is also obtained. A result of Basu is deduced as a particular case.     

Multiday expected shortfall under generalized t distributions: evidence from global stock market

Review of Quantitative Finance and Accounting - Earnings management research often uses discretionary accruals from Jones-type models. These models assume a linear relation between sales changes...     

VaR and ES for linear portfolios with mixture of generalized Laplace distributions risk factors

In this paper, we propose an explicit estimation of Value-at-Risk (VaR) and Expected Shortfall (ES) for linear portfolios when the risk factors change with a convex mixture of generalized Laplace distributions (M-GLD). We introduce the dynamics Delta-GLD-VaR, Delta-GLD-ES, Delta-MGLD-VaR and Delta-MGLD-ES, by using conditional correlation multivariate GARCH. The generalized Laplace distribution impose less restrictive assumptions during estimation that should improve the precision of the VaR and ES through the varying shape and fat tails of the risk factors in relation with the historical sample data. We also suggested some areas of application to measure price risk in agriculture, risk management and financial portfolio optimization.     

Convex risk measures based on generalized lower deviation and their applications

Considering the implementability and the properties that a reasonable and realistic risk measure should satisfy, we propose a new class of risk measures based on generalized lower deviation with respect to a chosen benchmark. Besides convexity and monotonicity, our new risk measure can reflect the investor's degree of risk aversion as well as the fat-tail phenomenon of the loss distribution with the help of different benchmarks and weighted functions. Based on the new risk measure, we establish a realistic portfolio selection model taking market frictions into account. To examine the influence of the benchmarks and weighted functions on the optimal portfolio and its performance, we carry out a series of empirical studies in Chinese stock markets. Our in-sample and out-of-sample results show that the new risk measure and the corresponding portfolio selection model can reflect the investor's risk averse attitude and the impact of different trading constraints. Most importantly, with the new risk measure we can obtain an optimal portfolio which is more robust and superior to the optimal portfolios obtained with the traditional expected shortfall risk measures.     

On the distribution of discounted loss reserves using generalized linear models

Renshaw and Verrall [] specified the generalized linear model (GLM) underlying the chain-ladder technique and suggested some other GLMs which might be useful in claims reserving. The purpose of this paper is to construct bounds for the discounted loss reserve within the framework of GLMs. Exact calculation of the distribution of the total reserve is not feasible, and hence the determination of lower and upper bounds with a simpler structure is a possible way out. The paper ends with numerical examples illustrating the usefulness of the presented approximations.     

Portfolio optimization under a generalized hyperbolic skewed t distribution and exponential utility

In this paper, we show that if asset returns follow a generalized hyperbolic skewed t distribution, the investor has an exponential utility function and a riskless asset is available, the optimal portfolio weights can be found either in closed form or using a successive approximation scheme. We also derive lower bounds for the certainty equivalent return generated by the optimal portfolios. Finally, we present a study of the performance of mean–variance analysis and Taylor’s series expected utility expansion (up to the fourth moment) to compute optimal portfolios in this framework.     

Modeling and forecasting expected shortfall with the generalized asymmetric Student-t and asymmetric exponential power distributions

Financial returns typically display heavy tails and some degree of skewness, and conditional variance models with these features often outperform more limited models. The difference in performance may be especially important in estimating quantities that depend on tail features, including risk measures such as the expected shortfall. Here, using recent generalizations of the asymmetric Student-t and exponential power distributions to allow separate parameters to control skewness and the thickness of each tail, we fit daily financial return volatility and forecast expected shortfall for the S&P 500 index and a number of individual company stocks; the generalized distributions are used for the standardized innovations in a nonlinear, asymmetric GARCH-type model. The results provide evidence for the usefulness of the general distributions in improving fit and prediction of downside market risk of financial assets. Constrained versions, corresponding with distributions used in the previous literature, are also estimated in order to provide a comparison of the performance of different conditional distributions.     

农业银行经营行人力资源优化配置问题研究

文章研究农业银行经营行人力资源及优化配置问题。     

On Tail Value-at-Risk for sums of non-independent random variables with a generalized Pareto distribution

Recently in actuarial literature several authors have derived lower and upper bounds in the sense of convex order for sums of random variables with given marginal distributions and unknown dependency structure. In this paper, we derive convex bounds for sums of non-independent and identically distributed random variables when marginal distributions are mixture models. In particular, we examine some well-known risk measures and we find approximations for Tail Value-at-Risk of the sums considered when marginal distributions are generalized Pareto distributions. By numerical examples we illustrate the goodness of the presented approximations.      

Assessing the predictive performance of artifIcial neural network‐based classifiers based on different data preprocessing methods,distributions and training mechanisms

We analyse the implications of three different factors (preprocessing method, data distribution and training mechanism) on the classification performance of artificial neural networks (ANNs). We use three preprocessing approaches: no preprocessing, division by the maximum absolute values and normalization. We study the implications of input data distributions by using five datasets with different distributions: the real data, uniform, normal, logistic and Laplace distributions. We test two training mechanisms: one belonging to the gradient‐descent techniques, improved by a retraining procedure, and the other is a genetic algorithm (GA), which is based on the principles of natural evolution. The results show statistically significant influences of all individual and combined factors on both training and testing performances. A major difference with other related studies is the fact that for both training mechanisms we train the network using as starting solution the one obtained when constructing the network architecture. In other words we use a hybrid approach by refining a previously obtained solution. We found that when the starting solution has relatively low accuracy rates (80–90%) the GA clearly outperformed the retraining procedure, whereas the difference was smaller to non‐existent when the starting solution had relatively high accuracy rates (95–98%). As reported in other studies, we found little to no evidence of crossover operator influence on the GA performance. Copyright © 2005 John Wiley & Sons, Ltd.     

Simultaneous estimation of the location and scale parameters of the gamma distribution by linear functions of order statistics

Summary

Large sample estimation of the origin (α₁ and the scale parameter (α₂ of the gamma distribution when the shape parameter m is known is considered. Assuming both parameters are unknown, the optimum spacings (0<λ₁<λ₂<...λ _k <1) determining the maximum efficiences among other choices of the same number of observations are obtained. The coefficients to be used in computing the estimates, their variances and their asymptotic relative efficiencies (A.R.E.) relative to the Cramer Rao lower bounds are given.     

A note on generalized distortion risk measures

A generalized distortion risk measure is introduced as power of the mean absolute deviation power of a distorted random variable with respect to a location parameter. This class of risk measures extends both the distortion risk measure by Wang and Denneberg and the class of financial risk measures by Pedersen and Satchell, which itself contains the class of Stone. Integral representations and a stop–loss order preserving property of a special up-side risk measure are derived.