Applied Stochastic Models in Business and Industry

Bahsoun, Wael; Góra, Paweł; Mayoral, Silvia; Morales, Manuel

2007 Applied Stochastic Models in Business and Industry

doi: 10.1002/asmb.663

We introduce a general binomial model for asset prices based on the concept of random maps. The asymptotic stationary distribution for such model is studied using techniques from dynamical systems. In particular, we present a technique to construct a general binomial model with a predetermined stationary distribution. This technique is independent of the chosen distribution making our model potentially useful in financial applications. We briefly explore the suitability of our construction as an implied binomial tree. Copyright © 2006 John Wiley & Sons, Ltd.

Gill, Avninder; Ishaq Bhatti, M.

2007 Applied Stochastic Models in Business and Industry

doi: 10.1002/asmb.666

Warehouse location and retailer allocation is a high‐level strategic decision problem that is commonly encountered by logisticians and supply chain managers, especially during the supply chain design phase. Considering the product distribution cost and warehouse capital cost trade‐offs, this paper models the warehouse location and retailer allocation problem as a 0–1 integer programming problem and provides an efficient two‐stage set covering heuristic algorithm to solve large‐sized problems. Finally, concluding remarks and some recommendations for further research are also presented. Copyright © 2007 John Wiley & Sons, Ltd.

Weißbach, Rafael; Dette, Holger

2007 Applied Stochastic Models in Business and Industry

doi: 10.1002/asmb.667

In banking, the default behaviour of the counterpart is not only of interest for the pricing of transactions under credit risk but also for the assessment of a portfolio credit risk. We develop a test against the hypothesis that default intensities are chronologically constant within a group of similar counterparts, e.g. a rating class. The Kolmogorov–Smirnov‐type test builds up on the asymptotic normality of counting processes in event history analysis. The right censoring accommodates for Markov processes with more than one no‐absorbing state. A simulation study and two examples of rating systems demonstrate that partial homogeneity can be assumed, however occasionally, certain migrations must be modelled and estimated inhomogeneously. Copyright © 2007 John Wiley & Sons, Ltd.

Li, Zehui; Kong, Xinbing

2007 Applied Stochastic Models in Business and Industry

doi: 10.1002/asmb.669

In this paper, we construct a new risk model based on the policy entrance process. The model is concerned with n kinds of independent policies, and each policy is allowed to claim more than once before it expires. As each kind of policy is issued according to a non‐homogeneous Poisson process, the long run behaviour of the new risk process is investigated. When the tail of the claim size distribution is regularly varying, the standardized risk process is proved to converge to a stable law. When each kind of policy is issued according to a homogeneous Poisson process, we also give a diffusion approximation of the new risk process. Copyright © 2007 John Wiley & Sons, Ltd.

Casarin, Roberto; Billio, Monica

2007 Applied Stochastic Models in Business and Industry

doi: 10.1002/asmb.671

One of the crucial aspects in asset allocation problems is the assumption concerning the probability distribution of asset returns. Financial managers generally suppose normal distribution, even if extreme realizations usually have an higher frequency than in the Gaussian case. The aim of this paper is to propose a general Monte Carlo simulation approach able to solve an asset allocation problem with shortfall constraint, and to evaluate the exact portfolio risk‐level when managers assume a misspecified return behaviour. We assume that returns are generated by a multivariate skewed Student‐t distribution where each marginal can have different degrees of freedom. The stochastic optimization allows us to value the effective risk for managers. In the empirical application we consider a symmetric and heterogeneous case, and interestingly note that a multivariate Student‐t with heterogeneous marginal distributions produces in the optimization problem a shortfall probability and a shortfall return level that can be adequately approximated by assuming a multivariate Student‐t with common degrees of freedom. Thus, the proposed simulation‐based approach could be an important instrument for investors who require a qualitative assessment of the reliability and sensitivity of their investment strategies in the case their models could be potentially misspecified. Copyright © 2007 John Wiley & Sons, Ltd.