Saddlepoint approximations to the mean and variance of the extended hypergeometric distribution

Conditional inference on 2 x 2 tables with fixed margins and unequal probabilities is based on the extended hypergeometric distribution. If the support of the distribution is large, exact calculation of the conditional mean and variance of the table entry may be computationally demanding. This paper proposes a single‐saddlepoint approximation to the mean and variance. While the approximation achieves acceptable accuracy for ordinary practical purposes, an alternative saddlepoint approximation is provided that gives much closer to exact results. It improves the accuracy of current approximations to up to more than four powers of ten.     

聚合信用风险模型的改进和研究

近年来的研究发现,违约损失率的分布呈现一种双峰特征。文章对传统聚合信用风险模型进行改进,用具有双峰特征的双beta分布来刻画违约损失率的变化,给出全部贷款组合信用风险概率生成函数的解析式,利用数值模拟的结果验证了模型的有效性。     

Bayesian Statistical Computations of Nonlinear Financial Time Series Models: A Survey with Illustrations

A survey of Bayesian statistical computations of quadratureformula, Laplace approximation, and Markov Chain Monte Carlo algorithms ispresentedand their applications to nonlinear financial time series models arediscussed.     

A new higher-order weak approximation scheme for stochastic differential equations and the Runge–Kutta method

The authors report on the construction of a new algorithm for the weak approximation of stochastic differential equations. In this algorithm, an ODE-valued random variable whose average approximates the solution of the given stochastic differential equation is constructed by using the notion of free Lie algebras. It is proved that the classical Runge–Kutta method for ODEs is directly applicable to the ODE drawn from the random variable. In a numerical experiment, this is applied to the problem of pricing Asian options under the Heston stochastic volatility model. Compared with some other methods, this algorithm is significantly faster. This research was partly supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Scientific Research (C), 15540110, 2003 and 18540113, 2006, the 21st century COE program at Graduate School of Mathematical Sciences, the University of Tokyo, and JSPS Core-to-Core Program 18005.     

基于线性相位近似的SOQPSK-TG信号同步算法

SOQPSK-TG （Telemetry Group version of Shaped Offset Quadrature Phase Shift Key）具有良好的频率利用率和功率利用率,广泛应用于无线通信系统当中。在连续通信模式下,SOQPSK-TG信号的同步主要采用直接判决算法。为进一步降低算法复杂度,推导了基于线性相位近似的最大似然估计误差鉴别器,理论上分析了算法估计性能,并搭建了简化的接收模型。通过仿真证明了算法在估计性能上优于脉冲幅度调制方法,算法误码率接近理论性能。     

Spatial statistical modelling of insurance risk: a spatial epidemiological approach to car insurance

Spatial models, such as the Besag, York and Mollie (BYM) model, have long been used in epidemiology and disease mapping. A common research question in these subjects is modelling the number of disease events per region; here the BYM models provides a holistic framework for both covariates and dependencies between regions. We use these tools to assess the relative insurance risk associated with the policyholders geographical location. A Bayesian modelling approach is presented and an elastic net is used to reduce the large number of possible geographic covariates. The final inference is performed using Integrated Nested Laplace Approximation. The model is applied to car insurance data from If P&C Insurance together with spatially referenced covariate data of high resolution, provided by Insightone. The entire analysis is performed using freely available R-packages. Including spatial dependence when modelling the number of claims significantly improves on the result obtained using ordinary generalised linear models. However, the support for adding a spatial component to the model for claims cost is weaker.     

Valuation of forward start options under affine jump-diffusion models

Under the general affine jump-diffusion framework of Duffie et al. [Econometrica, 2000, 68, 1343–1376], this paper proposes an alternative pricing methodology for European-style forward start options that does not require any parallel optimization routine to ensure square integrability. Therefore, the proposed methodology is shown to possess a better accuracy–efficiency trade-off than the usual and more general approach initiated by Hong [Forward Smile and Derivative Pricing. Working paper, UBS, 2004] that is based on the knowledge of the forward characteristic function. Explicit pricing solutions are also offered under the nested jump-diffusion setting proposed by Bakshi et al. [J. Finance, 1997, 52, 2003–2049], which accommodates stochastic volatility and stochastic interest rates, and different integration schemes are numerically tested.     

Conditional risk measures in a bipartite market structure

In this paper, we study the effect of network structure between agents and objects on measures for systemic risk. We model the influence of sharing large exogeneous losses to the financial or (re)insurance market by a bipartite graph. Using Pareto-tailed losses and multivariate regular variation, we obtain asymptotic results for conditional risk measures based on the Value-at-Risk and the Conditional Tail Expectation. These results allow us to assess the influence of an individual institution on the systemic or market risk and vice versa through a collection of conditional risk measures. For large markets, Poisson approximations of the relevant constants are provided. Differences of the conditional risk measures for an underlying homogeneous and inhomogeneous random graph are illustrated by simulations.     

Analysis of Error with Malliavin Calculus: Application to Hedging

The aim of this paper is to compute the quadratic error of a discrete time-hedging strategy in a complete multidimensional model. This result extends that of Gobet and Temam (2001) and Zhang (1999) . More precisely, our basic assumption is that the asset prices satisfy the d -dimensional stochastic differential equation   dXⁱ_t = Xⁱ_t ( bⁱ ( X_t ) dt +σ _{i , j} ( X_t ) dW^j_t )  . We precisely describe the risk of this strategy with respect to n , the number of rebalancing times. The rates of convergence obtained are     for any options with Lipschitz payoff and  1/ n ^1/4  for options with irregular payoff.     

On a stochastic approximation procedure based on averaging

Based on the idea of averaging a new stochastic approximation algorithm has been proposed by Bather (1989), which shows a preferable performance for small to moderate sample sizes. In the present paper an almost sure representation is established for this procedure, which gives the optimal rate of convergence with minimal asymptotic variance. Work partly supported by the research grant Ku719/2-1 of the Deutsche Forschungsgemeinschaft