Explicit computations for some Markov modulated counting processes

In this paper we present elementary computations for some Markov modulated counting processes, also called counting processes with regime switching. Regime switching has become an increasingly popular concept in many branches of science. In finance, for instance, one could identify the background process with the `state of the economy', to which asset prices react, or as an identification of the varying default rate of an obligor. The key feature of the counting processes in this paper is that their intensity processes are functions of a finite state Markov chain. This kind of processes can be used to model default events of some companies. Many quantities of interest in this paper, like conditional characteristic functions, can all be derived from conditional probabilities, which can, in principle, be analytically computed. We will also study limit results for models with rapid switching, which occur when inflating the intensity matrix of the Markov chain by a factor tending to infinity. The paper is largely expository in nature, with a didactic flavor

ERP analysis of cognitive sequencing : a left-anterior negativity related to structural transformation processing

A major objective of cognitive neuroscience is to identify those neurocomputational processes that may be shared by multiple cognitive functions vs those that are highly specifc. This problem of identifying general vs specialized functions is of particular interest in the domain of language processing. Within this domain, event related brain potential (ERP) studies have demonstrated a left anterior negativity (LAN) in a range 300 to 700 ms, associated with syntactic processing, often linked to grammatical function words. These words have little or no semantic content, but rather play a role in encoding syntactic structure required for parsing. In the current study we test the hypothesis that the LAN reflects the operation of a more general sequence processing capability in which special symbols encode structural information that, when combined with past elements in the sequence, allows the prediction of successor elements. We recorded ERPs during a non-linguistic sequencing task that required subjects (nà10) to process special symbols possessing the functional property defined above. When compared to ERPs in a control condition, function symbol processing elicits a left anterior negative shift between with temporal and spatial characteristics quite similar to the LAN described during function word processing in language, supporting our hypothesis. These results are discussed in the context of related studies of syntactic and cognitive sequence processing

Extreme Moves in Foreign Exchange Rates and Risk Limit Setting

Foreign exchange rates can be subject to considerable daily fluctuations (up to 5 percent within one day). This can, in certain cases, cause serious losses on open overnight positions. Given a maximum tolerable loss for a company, limits have to be set on open overnight positions in foreign currencies. Usually, these limits are determined by using a normal ("Gaussian") model for the daily fluctuations. In our study we illustrate how this common model sometimes quite strongly underestimates the actual extreme risks and, based on methods from the Extreme Value Theory (EVT), we propose and justify a more accurate model.extreme value theory, risk management, foreign exchange, time series analysis

The Fr\"olicher-Nijenhuis bracket for derivation based non commutative differential forms

In commutative differential geometry the Fr\"olicher-Nijenhuis bracket computes all kinds of curvatures and obstructions to integrability. In \cit!{3} the Fr\"olicher-Nijenhuis bracket was developped for universal differential forms of non-commutative algebras, and several applications were given. In this paper this bracket and the Fr\"olicher-Nijenhuis calculus will be developped for several kinds of differential graded algebras based on derivations, which were indroduced by \cit!{6}.Comment: AmSTeX, 28 pages, ESI Preprint 13

Large deviations for Markov-modulated diffusion processes with rapid switching

In this paper, we study small noise asymptotics of Markov-modulated diffusion processes in the regime that the modulating Markov chain is rapidly switching. We prove the joint sample-path large deviations principle for the Markov-modulated diffusion process and the occupation measure of the Markov chain (which evidently also yields the large deviations principle for each of them separately by applying the contraction principle). The structure of the proof is such that we first prove exponential tightness, and then establish a local large deviations principle (where the latter part is split into proving the corresponding upper bound and lower bound)

Corporate decision-making in R&D outsourcing and the impact on internal R&D employment intensity

This article aims to assess whether firms’ strategies of R&D outsourcing determine changes in their internal R&D employment intensity. Four strategic decisions are investigated: to start, increase, decrease or stop outsourcing. It is found that internal R&D employment intensity decreases when firms decide to start, to increase, or to stop R&D outsourcing. However, this finding hides important differences according to the type and the location of the contractor. In general, firms prefer a mix of different types of contractors at different locations. Started outsourcing of R&D to research centers within the nation and increased R&D outsourcing to research centers within the region appear to decrease the internal R&D employment intensity. Decreasing outsourcing to national universities in another region also has a negative impact on internal R&D employment intensity. A corporate decision to stop R&D outsourcing to other firms within the nation but outside the region has a positive impact on the internal R&D employment intensity. The latter is the only effect that is not only statistically significant but is also substantial in magnitude

Sample-path Large Deviations in Credit Risk

The event of large losses plays an important role in credit risk. As these large losses are typically rare, and portfolios usually consist of a large number of positions, large deviation theory is the natural tool to analyze the tail asymptotics of the probabilities involved. We first derive a sample-path large deviation principle (LDP) for the portfolio's loss process, which enables the computation of the logarithmic decay rate of the probabilities of interest. In addition, we derive exact asymptotic results for a number of specific rare-event probabilities, such as the probability of the loss process exceeding some given function

Dynamic Financial Analysis - Understanding Risk and Value Creation in Insurance

The changing business environment in non-life insurance and reinsurance has raised the need for new quantitative methods to analyze the impact of various types of strategic decisions on a company’s bottom line. Dynamic Financial Analysis («DFA») has become popular among practitioners as a means of addressing these new requirements. It is a systematic approach based on large-scale computer simulations for the integrated financial modeling of non-life insurance and reinsurance companies aimed at assessing the risks and the benefits associated with strategic decisions. DFA allows decision makers to understand and quantify the impact and interplay of the various risks that their company is exposed to, and – ultimately – to make better informed strategic decisions. In this brochure, we provide an overview and assessment of the state of the industry related to DFA. We investigate the DFA value proposition, we explain its elements and we explore its potential and limitations.reinsurance, dynamic financial analysis, insurance

Computing Integer Powers in Floating-Point Arithmetic

We introduce two algorithms for accurately evaluating powers to a positive integer in floating-point arithmetic, assuming a fused multiply-add (fma) instruction is available. We show that our log-time algorithm always produce faithfully-rounded results, discuss the possibility of getting correctly rounded results, and show that results correctly rounded in double precision can be obtained if extended-precision is available with the possibility to round into double precision (with a single rounding).Comment: Laboratoire LIP : CNRS/ENS Lyon/INRIA/Universit\'e Lyon