Saddlepoint approximations for the sum of independent non‐identically distributed binomial random variables

We discuss saddlepoint approximations to the distribution of the sum of independent non‐identically distributed binomial random variables. We examine the accuracy of the saddlepoint methods for a sum of 10 binomials with different sets of parameter values. The numerical results indicate that the saddlepoint approximations provide very accurate estimates for the probability mass function and the right‐tail probabilities for the cumulative distribution function of the sum.     

邻域关系下的覆盖粗糙集及其模糊性度量

对邻域关系下的覆盖粗糙集的矩阵描述及模糊性度量进行分析和研究。首先,给出了一种新的邻域关系的覆盖粗糙集上、下近似的定义。其次,在邻域关系下的覆盖近似空间引入了一类新的模糊集,得覆盖近似空间的模糊性度量,最后通过实例给出直观解释。     

The pricing of basket-spread options

Since the pioneering paper of Black and Scholes was published in 1973, enormous research effort has been spent on finding a multi-asset variant of their closed-form option pricing formula. In this paper, we generalize the Kirk [Managing Energy Price Risk, 1995] approximate formula for pricing a two-asset spread option to the case of a multi-asset basket-spread option. All the advantageous properties of being simple, accurate and efficient are preserved. As the final formula retains the same functional form as the Black–Scholes formula, all the basket-spread option Greeks are also derived in closed form. Numerical examples demonstrate that the pricing and hedging errors are in general less than 1% relative to the benchmark results obtained by numerical integration or Monte Carlo simulation with 10 million paths. An implicit correction method is further applied to reduce the pricing errors by factors of up to 100. The correction is governed by an unknown parameter, whose optimal value is found by solving a non-linear equation. Owing to its simplicity, the computing time for simultaneous pricing and hedging of basket-spread option with 10 underlying assets or less is kept below 1 ms. When compared against the existing approximation methods, the proposed basket-spread option formula coupled with the implicit correction turns out to be one of the most robust and accurate methods.     

Approximating functionals of local martingales under lack of uniqueness of the Black–Scholes PDE solution

When the underlying stock price is a strict local martingale process under an equivalent local martingale measure, the Black–Scholes PDE associated with a European option may have multiple solutions. In this paper, we study an approximation for the smallest hedging price of such an European option. Our results show that a class of rebate barrier options can be used for this approximation. Among them, a specific rebate option is also provided with a continuous rebate function, which corresponds to the unique classical solution of the associated parabolic PDE. Such a construction makes existing numerical PDE techniques applicable for its computation. An asymptotic convergence rate is also studied when the knock-out barrier moves to infinity under suitable conditions.     

PORTFOLIO SELECTION WITH MONOTONE MEAN-VARIANCE PREFERENCES

We propose a portfolio selection model based on a class of monotone preferences that coincide with mean-variance preferences on their domain of monotonicity, but differ where mean-variance preferences fail to be monotone and are therefore not economically meaningful. The functional associated with this new class of preferences is the best approximation of the mean-variance functional among those which are monotonic. We solve the portfolio selection problem and we derive a monotone version of the capital asset pricing model (CAPM), which has two main features: (i) it is, unlike the standard CAPM model, arbitrage free, (ii) it has empirically testable CAPM-like relations. The monotone CAPM has thus a sounder theoretical foundation than the standard CAPM and a comparable empirical tractability.     

A new test for analysing hysteresis in European unemployment

This article proposes a new unit root test to analyse unemployment hysteresis. The test is able to incorporate cross-sectional dependence, unattended nonlinearity and unknown structural breaks in the time-series data. This study used data on unemployment in five European countries. The findings indicated that conventional unit root tests failed to reject the null hypothesis of hysteresis for all countries. However, the newly proposed unit root test was able to reject the null hypothesis for the Spanish unemployment rate.     

A hybrid decomposition algorithm for designing a multi-modal transportation network under biomass supply uncertainty

This study presents a two-stage stochastic programming model for the design and management of a biomass co-firing supply chain network under feedstock supply uncertainty. To represent a more realistic case, we generate scenarios from prediction errors of the historical and forecasted biomass supply availabilities. We solve the model using a hybrid decomposition algorithm that combines Sample average approximation with an enhanced Progressive hedging algorithm. The proposed algorithm is validated via a real-world case study using data from Mississippi and Alabama. Computational results indicate that the proposed algorithm is capable of producing high quality solutions in a reasonable amount of time.     

A panel stationarity test with gradual structural shifts: Re-investigate the international commodity price shocks

This paper proposes a simple panel stationarity test which takes into account structural shifts and cross-section dependency. Structural shifts are modelled as gradual/smooth process with a Fourier approximation. The so-called Fourier panel stationarity test has a standard normal distribution. The Monte Carlo simulations indicate that (i) if the error terms are i.i.d, the test shows good size and power properties even in small samples; and (ii) if the error terms are serially correlated, the test has reasonable size and high power. We re-examine the behavior of the international commodity prices and find out an evidence on the persistence of shocks.     

KMT-type inequalities and goodness-of-fit tests

The implications of the probability inequality of Komløs, Major and Tusnády (1975) for the theory of goodness-of-fit tests, especially tests based on stochastic integrals with respect to the basic martingale in the random censoring model, are discussed. Choices of the integrand of the stochastic integral which yield highly efficient generalized rank and supremum type tests are given for the simple as well as the composite null hypothesis.     

A new sequential design based on the robbins-monro procedure

Summary A sequential estimation procedure based on the Robbins-Monro process is proposed. Through observations of a random variableY(x), estimates of a regression functionM(x) are obtained, whereM(x)=E[Y(x)]. The estimates of the roots ofM(x) are shown to be strongly convergent and asymptotically normal with minimum variance.