Matematické teorie pojišťování
Maximum likelihood estimator of the volatility of forward rates driven by geometric spatial AR sheet.
Model tracking for risk problems.
Modèle de reconstitution de l'évolution démographique intercensitaire en milieu urbain
Modelling financial time series using reflections of copulas
We have intensified studies of reflections of copulas (that we introduced recently in [6]) and found that their convex combinations exhibit potentially useful fitting properties for original copulas of the Normal, Frank, Clayton and Gumbel types. We show that these properties enable us to construct interesting models for the relations between investment in stocks and gold.
Models for stochastic mortality
This paper is an attempt to present and analyse stochastic mortality models. We propose a couple of continuous-time stochastic models that are natural generalizations of the Gompertz law in the sense that they reduce to the Gompertz function when the volatility parameter is zero. We provide a statistical analysis of the available demographic data to show that the models fit historical data well. Finally, we give some practical examples for the multidimensional models.
More general credibility models
This communication gives some extensions of the original Bühlmann model. The paper is devoted to semi-linear credibility, where one examines functions of the random variables representing claim amounts, rather than the claim amounts themselves. The main purpose of semi-linear credibility theory is the estimation of (the net premium for a contract with risk parameter ) by a linear combination of given functions of the observable variables: . So the estimators mainly considered here are linear...
Multistage multivariate nested distance: An empirical analysis
Multistage stochastic optimization requires the definition and the generation of a discrete stochastic tree that represents the evolution of the uncertain parameters in time and space. The dimension of the tree is the result of a trade-off between the adaptability to the original probability distribution and the computational tractability. Moreover, the discrete approximation of a continuous random variable is not unique. The concept of the best discrete approximation has been widely explored and...
Multivariate extensions of expectiles risk measures
This paper is devoted to the introduction and study of a new family of multivariate elicitable risk measures. We call the obtained vector-valued measures multivariate expectiles. We present the different approaches used to construct our measures. We discuss the coherence properties of these multivariate expectiles. Furthermore, we propose a stochastic approximation tool of these risk measures.
Multivariate Fréchet copulas and conditional value-at-risk.
Multivariate nonlinear analysis and prediction of Shanghai stock market.
Multivariate smooth transition AR model with aggregation operators and application to exchange rates
An overview of multivariate modelling based on logistic and exponential smooth transition models with transition variable generated by aggregation operators and orders of auto and exogenous regression selected by information criterion separately for each regime is given. Model specification procedure is demonstrated on trivariate exchange rates time series. The application results show satisfactory improvement in fit when particular aggregation operators are used. Source code in the form of Mathematica...
New variance ratio tests to identify random walk from the general mean reversion model.
On Conditional Value at Risk (CoVaR) for tail-dependent copulas
The paper deals with Conditional Value at Risk (CoVaR) for copulas with nontrivial tail dependence. We show that both in the standard and the modified settings, the tail dependence function determines the limiting properties of CoVaR as the conditioning event becomes more extreme. The results are illustrated with examples using the extreme value, conic and truncation invariant families of bivariate tail-dependent copulas.
On cumulative process model and its statistical analysis
The notion of the counting process is recalled and the idea of the ‘cumulative’ process is presented. While the counting process describes the sequence of events, by the cumulative process we understand a stochastic process which cumulates random increments at random moments. It is described by an intensity of the random (counting) process of these moments and by a distribution of increments. We derive the martingale – compensator decomposition of the process and then we study the estimator of the...
On maximum increase and decrease of brownian motion
On modelling long term stock returns with ergodic diffusion processes: arbitrage and arbitrage-free specifications.
On optimal credibility premiums in multiperiod insurance
This paper focuses on the problem of optimal arrangement of a stream of premiums in a multiperiod credibility model. On the basis of a given claim history (screening) and some individual information unknown to the insurance company (signaling), we derive the optimal streams in the case when the coverage period is not necessarily fixed, e.g., because of lapses, renewals, deaths, total losses, etc.
On risk minimizing strategies for default-free bond portfolio immunization
This paper presents new strategies for bond portfolio immunization which combine the time-honored duration with the M-Absolute measure defined by Nawalkha and Chambers (1996). The innovation consists in considering an average shock in a fixed time period as a random variable with mean μ or, alternatively, with normal distribution with mean μ and variance σ². Additionally, an extension to arbitrage free models of polynomial shocks is provided. Moreover, the Fisher and Weil model, the M-Absolute strategy...
On robust GMM estimation with applications in economics and finance
Generalized Methods of Moments (GMM) estimators are a popular tool in econometrics since introduced by Hansen (1982), because this approach provides feasible solutions for many problems present in economic data where least squares or maximum likelihood methods fail when naively applied. These problems may arise in errors-in-variable regression, estimation of labor demand curves, and asset pricing in finance, which are discussed here. In this paper we study a GMM estimator for the rank modelingapproach...