Social networks contain clusters of nodes centered at high-degree nodes and surrounded by low-degree nodes. Such a cluster structure of the networks is caused by the dependence (social relationships and interests) between nodes and possibly by heavytailed distributions of the node degrees. We consider the degree sequences generated by PageRank type sampling processes and investigate clusters of...

In this paper, we provide a new proof of the result that option prices are increasing in volatility when the underlying is a diffusion process. This has been shown to hold for convex payoff, path-independent options by El Karoui et al [7], Hobson [12] amongst others. The advantage of the new proof is that it can be extended to establish monotonicity results for path-dependent payoffs where the ...

Since its introduction, the Lee Carter model has been widely adopted as a means of modelling the distribution of projected mortality rates. Increasingly attention is being placed on alternative models and, importantly in the financial and actuarial literature, on models suited to risk management and pricing. Financial economic approaches based on term structure models provide a framework for em...

Wind power has seen strong growth over the last decade and increasingly affects electricity spot prices. Generation from wind energy is stochastic, and if there is lot of wind, prices tend to be lower. Therefore, for an investor, but also for the whole electricity system, it is important to assess the value of wind power at different locations. In this paper, we develop a stochastic simulation ...

Stochastic generation, i.e. electrical power production by an uncontrolled primary energy source, is expected to play an important role in future power systems. A new power system structure is created due to the largescale implementation of this small-scale, distributed, nondispatchable generation; the ’horizontally operated’ system. Modelling methodologies that can deal with the operational un...

The paper considers empirical distribution functions of stationary causal processes. Weak convergence of normalized empirical distribution functions to Gaussian processes is established and sample path properties are discussed. The Chibisov-O’Reilly Theorem is generalized to dependent random variables. The proposed dependence structure is related to the sensitivity measure, a quantity appearing...

In this paper we work in the framework of a k-dimensional vector of log-linear risks. Under weak conditions on the marginal tails and the dependence structure of a vector of positive risks we derive the asymptotic tail behaviour of the aggregated risk and present an application concerning log-normal risks with stochastic volatility.

In this paper we work in the framework of a k-dimensional vector of log-linear risks. Under weak conditions on the marginal tails and the dependence structure of a vector of positive risks, we derive the asymptotic tail behaviour of the aggregated risk and present an application concerning log-normal risks with stochastic volatility.

We consider nonparametric estimation of mean regression and conditional variance (or volatility) functions in nonlinear stochastic regression models. Simultaneous confidence bands are constructed and the coverage probabilities are shown to be asymptotically correct. The imposed dependence structure allows applications in many linear and nonlinear auto-regressive processes. The results are appli...