Search results for "Stochastic process"
showing 10 items of 346 documents
Properties of the elasticity of a continuous random variable. A special look at its behavior and speed of change
2016
ABSTRACTBelzunce et al. (1995) define the elasticity for non negative random variables as the reversed proportional failure rate (RPFR). Veres-Ferrer and Pavia (2012, 2014b) interpret it in economic terms, extending its definition to variables that can also take negative values, and briefly present the role of elasticity in characterizing probability distributions. This paper highlights a set of properties demonstrated by elasticity, which shows many similar properties to the reverse hazard function. This paper pays particular attention to studying the increase/decrease and the speed of change of the elasticity function. These are important properties because of the characterizing role of e…
The Risk Premium and the Esscher Transform in Power Markets
2012
In power markets one frequently encounters a risk premium being positive in the short end of the forward curve, and negative in the long end. Economically it has been argued that the positive premium is reflecting retailers aversion for spike risk, wheras in the long end of the forward curve the hedging pressure kicks in as in other commodity markets. Mathematically, forward prices are expressed as risk-neutral expectations of the spot at delivery. We apply the Esscher transform on power spot models based on mean-reverting processes driven by independent increment (time-inhomogeneous Levy) processes. It is shown that the Esscher transform is yielding a change of mean-reversion level. Moreov…
Weather Derivatives and Stochastic Modelling of Temperature
2011
We propose a continuous-time autoregressive model for the temperature dynamics with volatility being the product of a seasonal function and a stochastic process. We use the Barndorff-Nielsen and Shephard model for the stochastic volatility. The proposed temperature dynamics is flexible enough to model temperature data accurately, and at the same time being analytically tractable. Futures prices for commonly traded contracts at the Chicago Mercantile Exchange on indices like cooling- and heating-degree days and cumulative average temperatures are computed, as well as option prices on them.
Isotropic stochastic flow of homeomorphisms on Rd associated with the critical Sobolev exponent
2008
Abstract We consider the critical Sobolev isotropic Brownian flow in R d ( d ≥ 2 ) . On the basis of the work of LeJan and Raimond [Y. LeJan, O. Raimond, Integration of Brownian vector fields, Ann. Probab. 30 (2002) 826–873], we prove that the corresponding flow is a flow of homeomorphisms. As an application, we construct an explicit solution, which is also unique in a certain space, to the stochastic transport equation when the associated Gaussian vector fields are divergence free.
Flow of Homeomorphisms and Stochastic Transport Equations
2007
Abstract We consider Stratonovich stochastic differential equations with drift coefficient A 0 satisfying only the condition of continuity where r is a positive C 1 function defined on a neighborhood ]0, c 0] of 0 such that (Osgood condition), and s → r(s) is decreasing while s → sr(s 2) is increasing. We prove that the equation defines a flow of homeomorphisms if the diffusion coefficients A 1,…, A N are in . If , we prove limit theorems for Wong–Zakai approximation as well as for regularizing the drift A 0. As an application, we solve a class of stochastic transport equations.
Stochastic dynamics of leukemic cells under an intermittent targeted therapy
2009
The evolutionary dynamics of cancerous cell populations in a model of Chronic Myeloid Leukemia (CML) is investigated in the presence of an intermittent targeted therapy. Cancer development and progression is modeled by simulating the stochastic evolution of initially healthy cells which can experience genetic mutations and modify their reproductive behavior, becoming leukemic clones. Front line therapy for the treatment of patients affected by CML is based on the administration of tyrosine kinase inhibitors, namely imatinib (Gleevec) or, more recently, dasatinib or nilotinib. Despite the fact that they represent the first example of a successful molecular targeted therapy, the development o…
Modeling the coupled return-spread high frequency dynamics of large tick assets
2015
Large tick assets, i.e. assets where one tick movement is a significant fraction of the price and bid-ask spread is almost always equal to one tick, display a dynamics in which price changes and spread are strongly coupled. We introduce a Markov-switching modeling approach for price change, where the latent Markov process is the transition between spreads. We then use a finite Markov mixture of logit regressions on past squared returns to describe the dependence of the probability of price changes. The model can thus be seen as a Double Chain Markov Model. We show that the model describes the shape of return distribution at different time aggregations, volatility clustering, and the anomalo…
Estimating the decomposition of predictive information in multivariate systems
2015
In the study of complex systems from observed multivariate time series, insight into the evolution of one system may be under investigation, which can be explained by the information storage of the system and the information transfer from other interacting systems. We present a framework for the model-free estimation of information storage and information transfer computed as the terms composing the predictive information about the target of a multivariate dynamical process. The approach tackles the curse of dimensionality employing a nonuniform embedding scheme that selects progressively, among the past components of the multivariate process, only those that contribute most, in terms of co…
Large deviations results for subexponential tails, with applications to insurance risk
1996
AbstractConsider a random walk or Lévy process {St} and let τ(u) = inf {t⩾0 : St > u}, P(u)(·) = P(· | τ(u) < ∞). Assuming that the upwards jumps are heavy-tailed, say subexponential (e.g. Pareto, Weibull or lognormal), the asymptotic form of the P(u)-distribution of the process {St} up to time τ(u) is described as u → ∞. Essentially, the results confirm the folklore that level crossing occurs as result of one big jump. Particular sharp conclusions are obtained for downwards skip-free processes like the classical compound Poisson insurance risk process where the formulation is in terms of total variation convergence. The ideas of the proof involve excursions and path decompositions for Mark…
Stochastic resonance and noise delayed extinction in a model of two competing species
2003
We study the role of the noise in the dynamics of two competing species. We consider generalized Lotka-Volterra equations in the presence of a multiplicative noise, which models the interaction between the species and the environment. The interaction parameter between the species is a random process which obeys a stochastic differential equation with a generalized bistable potential in the presence of a periodic driving term, which accounts for the environment temperature variation. We find noise-induced periodic oscillations of the species concentrations and stochastic resonance phenomenon. We find also a nonmonotonic behavior of the mean extinction time of one of the two competing species…