Supporting strategic conversations: the significance of a quantitative model building process

This paper reports on the use of a quantitative system dynamics simulation model building process that followed on from a ‘soft OR’ strategy making intervention with a top management team. The work was carried out for the Chief Constable and top team of a UK police force. The output of the ‘soft OR’ strategy making process provided the reason for, and so focus of, the simulation model. The focus of the strategic conversation was on exploring the tension between the supply of resources (in this case police officers) and the demands placed on those officers. The project involved a series of strategic conversations with members of the top team that were stimulated through the process of building a system dynamics model. The process was facilitated by two modellers—one focussing on managing the strategic enquiry, while the other considered the implications of the conversation for the construction of the system dynamics model. Through the process of gradually building the system dynamics model, a number of issues and lessons were raised for the development and delivery of effective strategy making and the strategic management of public organisations. In addition there were implications for operational research model building processes, especially when operating at senior levels and within a strategic context.     

On a singularity occurring in a self-correcting point process model

In a self-correcting point process model a boundary point of the parameter set is shown to be singular. This means a local behavior of the model which is qualitatively different from the LAN (or LAMN) condition satisfied at the other parameter points. As a consequence we obtain a nonnormal limiting distribution of the ML-estimator normalized with the random Fisher information.Work supported by a Heisenberg grant of the Deutsche Forschungsgemeinschaft.     

On the option valuation for a combined diffusion/point process model

This paper considers the price at time zero of a contingent claim when the price process is a diffusion/point process model. And we apply this price to European option.     

On selection of the order of the spectral density model for a stationary process

Summary Let {X(t)} be a stationary process with mean zero and spectral densityg(x). We shall use akth order parametric spectral modelf _τ(k) (x) for this process. Without Gaussianity we can obtain an estiamte of τ(k), say ĝt(k), by maximizing the quasi-Gaussian likelihood of this model. We can then construct the best linear predictor ofX(t), which is computed on the basis of the estimated spectral densityf _ĝt(k) (x). An asymptotic lower bound of the mean square error of the estimated predictor is obtained. The bound is attained ifk is selected by Akaike's information criterion.     

On optimal investment in a reinsurance context with a point process market model

We study an insurance model where the risk can be controlled by reinsurance and investment in the financial market. We consider a finite planning horizon where the timing of the events, namely the arrivals of a claim and the change of the price of the underlying asset(s), corresponds to a Poisson point process. The objective is the maximization of the expected total utility and this leads to a nonstandard stochastic control problem with a possibly unbounded number of discrete random time points over the given finite planning horizon. Exploiting the contraction property of an appropriate dynamic programming operator, we obtain a value-iteration type algorithm to compute the optimal value and strategy and derive its speed of convergence. Following Schäl (2004) we consider also the specific case of exponential utility functions whereby negative values of the risk process are penalized, thus combining features of ruin minimization and utility maximization. For this case we are able to derive an explicit solution. Results of numerical computations are also reported.     

On the quantitative sharpening of a theorem of birch

The author’s results concerning the null subspaces of arbitrary odd polynomials in several variables are generalized to the case of common null subspaces for several odd polynomials as well as to the complex case.     

On the exponential process associated with a CARMA-type process

We study the correlation decay and the expected maximal increments of the exponential processes determined by continuous-time autoregressive moving average (CARMA)-type processes of order (p, q). We consider two background driving processes, namely fractional Brownian motions and Lévy processes with exponential moments. The results presented in this paper are significant extensions of those very recent works on the Ornstein–Uhlenbeck-type case (p = 1, q = 0), and we develop more refined techniques to meet the general (p, q). In the concluding section, we discuss the perspective role of exponential CARMA-type processes in stochastic modelling of the burst phenomena in telecommunications and the leverage effect in financial econometrics.     

On a modification of the classical risk process

In this paper, we present the classical risk process with two-step premium function. This means that the gross risk premium rate changes if the insurer’s surplus reaches a certain threshold level. The formula for the infinite-time ruin probability is obtained. The asymptotic behaviour of the ruin probability in the case where the claim size distribution has a light tail is considered as well.     

On a generalization of the Richardson extrapolation process

Summary A convergence result for a generalized Richardson extrapolation process is improved upon considerably and additional results of interest are proved. An application of practical importance is also given. Finally, some known results concerning the convergence of Levin's T-transformation are reconsidered in light of the results of the present work.     

On a discrete version of the CIR process

We consider the so-called gambler's ruin problem for a discrete-time Markov chain that converges to a Cox–Ingersoll–Ross (CIR) process. Both the probability that the chain will hit a given boundary before the other and the average number of transitions needed to end the game are computed explicitly. Furthermore, we show that the quantities that we obtained tend to the corresponding ones for the CIR process. A real-life application to a problem in hydrology is presented.     

On the reverse process of a critical multitype Galton-Watson process without variances

Limit theorems are established for the reverse process of a critical multitype Galton-Watson process without variances. These results are an extension of those of Nakagawa |5| in the case with finite variances.     

On the quantitative subspace theorem

In this survey, we give an overview of recent improvements to the quantitative subspace theorem, obtained jointly with R. Ferretti, which follow from the work in [9]. Further, we give a new gap principle with which we can estimate the number of subspaces containing the “small solutions” of the systems of inequalities under consideration. As an introduction, we start with a quantitative version of Roth’s theorem. Bibliography: 28 titles.     

On a size-structured population model with infinite states-at-birth and distributed delay in birth process

In this article, we study a size-structured population model with infinite states-at-birth and distributed delay in birth process. We establish the well-posedness for this model and show that the solution of this model exhibits an asynchronous exponential growth by means of semigroups.