The Russian option: Finite horizon

We show that the optimal stopping boundary for the Russian option with finite horizon can be characterized as the unique solution of a nonlinear integral equation arising from the early exercise premium representation (an explicit formula for the arbitrage-free price in terms of the optimal stopping boundary having a clear economic interpretation). The results obtained stand in a complete parallel with the best known results on the American put option with finite horizon. The key argument in the proof relies upon a local time-space formula.Received: March 2004, Mathematics Subject Classification (2000): 91B28, 35R35, 45G10, 60G40, 60J60JEL Classification: G13Goran Peskir: Centre for Analytical Finance (funded by the Danish Social Science Research Council) and Network in Mathematical Physics and Stochastics (funded by the Danish National Research Foundation).The first draft of the present paper has been completed in September 2002. I am indebted to Albert Shiryaev for useful comments.     

Poisson–geometric INAR(1) process for modeling count time series with overdispersion

In this paper, we propose a new first‐order non‐negative integer‐valued autoregressive [INAR(1)] process with Poisson–geometric marginals based on binomial thinning for modeling integer‐valued time series with overdispersion. Also, the new process has, as a particular case, the Poisson INAR(1) and geometric INAR(1) processes. The main properties of the model are derived, such as probability generating function, moments, conditional distribution, higher‐order moments, and jumps. Estimators for the parameters of process are proposed, and their asymptotic properties are established. Some numerical results of the estimators are presented with a discussion of the obtained results. Applications to two real data sets are given to show the potentiality of the new process.     

A study on the competitive strategy of the universal postal service provider

We analysed how the universal postal service providers could employ their specificities to achieve an advantage over the growing competition. The basic input for the model is expert opinions. We interviewed 18 experts in five stages. As a multiple criteria decision support method, we used an analytic hierarchy process. Further, we proposed a geometric method for determining the business area where a company should focus its biggest attention to achieve the best result. By implementing the proposed model, a company should obtain two types of business directions, the first related to the proposed activities and the second to the business areas. To demonstrate the applicability of the proposed methodology, we tested and verified it in the case of the Serbian universal postal service provider which is a state-owned company called the Post of Serbia.     

Equilibrium compound distributions and stop-loss moments

A convolution representation is derived for the equilibrium or integrated tail distribution associated with a compound distribution. This result allows for the derivation of reliability properties of compound distributions, as well as an explicit analytic representation for the stop-loss premium, of interest in connection with insurance claims modelling. This result is extended to higher order equilibrium distributions, or equivalently to higher stop-loss moments. Special cases where the counting distribution is mixed Poisson or discrete phase-type are considered in some detail. An approach to handle more general counting distributions is also outlined.     

ON PORTFOLIO CHOICE BY MAXIMIZING THE OUTPERFORMANCE PROBABILITY

We consider the problem of optimal portfolio selection for a multidimensional geometric Brownian motion model. We look for portfolios that maximize the probability of outperforming a stochastic benchmark. More specifically, we seek to maximize the decay rate of the shortfall probability and (or) to minimize the decay rate of the outperformance probability in the long run. A simple heuristic enables us to find an asymptotically optimal investment policy. The results provide interesting insights.     

On the complete monotonicity of the compound geometric convolution with applications in risk theory

We prove that the complete monotonicity is preserved under mixed geometric compounding, and hence show that the ruin probability, the Laplace transform of the ruin time, and the density of the tail of the joint distribution of ruin and the deficit at ruin in the Sparre Andersen model are completely monotone if the claim size distribution has a completely monotone density.     

数控机床空间几何误差识别与检测

分析了国内外误差参数识别的方法,详细介绍了四线法识别和检测数控机床空间几何误差的过程和步骤,通过分析四线法的识别机床误差的工程,进一步识别数控机床空间几何误差的各项误差元素。为后续机床误差补偿提供理论依据。     

Edgeworth type expansion of ruin probability under Lévy risk processes in the small loading asymptotics

This paper presents an asymptotic expansion of the ultimate ruin probability under Lévy insurance risks as the loading factor tends to zero. The expansion formula is obtained via the Edgeworth type expansion for compound geometric distributions. We give higher-order expansion of the ruin probability, any order of which is available in explicit form, and discuss a certain type of validity of the expansion. We shall also give applications to evaluation of the VaR-type risk measure due to ruin, and the scale function of spectrally negative Lévy processes.     

PRICING AND HEDGING DOUBLE-BARRIER OPTIONS: A PROBABILISTIC APPROACH

Barrier options have become increasingly popular over the last few years. Less expensive than standard options, they may provide the appropriate hedge in a number of risk management strategies. In the case of a single-barrier option, the valuation problem is not very difficult (see Merton 1973 and Goldman, Sosin, and Gatto 1979). the situation where the option gets knocked out when the underlying instrument hits either of two well-defined boundaries is less straightforward. Kunitomo and Ikeda (1992) provide a pricing formula expressed as the sum of an infinite series whose convergence is studied through numerical procedures and suggested to be rapid. We follow a methodology which proved quite successful in the case of Asian options (see Geman and Yor 1992,1993) and which has its roots in some fundamental properties of Brownian motion. This methodology permits the derivation of a simple expression of the Laplace transform of the double-barrir price with respect to its maturity date. the inversion of the Laplace transform using techniques developed by Geman and Eydeland (1995), is then fairly easy to perform.     

一种基于自由度分析的过约束处理方法

特征造型是建立形体的产品信息模型,实现CAD/CAM一体化,支持设计和制造全过程的新兴造型技术。参数化设计可以使CAD系统具有交互式绘图功能以及自动绘图功能。参数化设计的关键是几何约束关系的提取和表达,几何约束的求解及参数化几何模型构造。约束求解是将特征间的相互依赖关系映射为几何或工程约束描述,通过求解约束实现设计对象的细节。本文提出了一种基于自由度分析的过约束处理方法。