The central result of this paper is the existence of limiting distributions for two classes of critical homogeneous-in-space branching processes with heavy tails spatial dynamics in dimension d = 2. In dimension d ≥ 3, the same results are true without any special assumptions on the underlying (non-degenerated) stochastic dynamics.

Iterative, opportunistic and evolving visual sense-making has been an important research topic as it assists users in overcoming ever-increasing information overload. Exploratory visualization systems (EVSs) maximize the amount of information users can gain through learning and have been widely used in scientific discovery and decision-making contexts. Although many EVSs have been developed recently, there is a lack of general guidance on how to evaluate such systems. Researchers face challenges such as understanding the cognitive learning process supported by these systems. In this paper, we present a formal user study on Newdle, a clustering-based EVS for large news collections, shedding light on a general methodology for EVS evaluation. Our approach is built upon cognitive load theory, which takes the user as well as the system as the focus of evaluation. The carefully designed procedures allow us to thoroughly examine the user’s cognitive process as well as control the variability among human subjects. Through this study, we analyse how and why clustering-based EVSs benefit (or hinder) users in a variety of information-seeking tasks. We also summarize leverage points for designing clustering-based EVSs.

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Counterparty credit risk has received increasing attention and become a topical issue since 2007 credit crisis, particularly for its impact on the valuation of the OTC derivatives. Credit Value Adjustment (CVA) has become an import field and it is required in Basel III. This paper studies CVA for European options under Bates model with stochastic default intensity. We develop a Monte Carlo and finite difference method framework for assessing exposure profiles and impact of counterparty credit risk in pricing. The exposures are computed by solving a partial integro-differential Equation (PIDE) using implicit-explicit (IMEX) time discretization schemes. CVA in presence of wrong way risk (WWR) is embedded in the correlation between risk factor and default intensity. Meanwhile, the jump-at-default feature of the models offers an effective means to assess WWR. Our results show that both jump and WWR play an important role in evaluating CVA and exposures. The impact is significant and it is crucial for risk management purpose.

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