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The self-normalized Donsker theorem revisited

Peter Parczewski

https://doi.org/10.15559/17-VMSTA82

Pub. online: 18 Sep 2017 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 4, Issue 3 (2017), pp. 189–198

Abstract

We extend the Poincaré–Borel lemma to a weak approximation of a Brownian motion via simple functionals of uniform distributions on n-spheres in the Skorokhod space $D([0,1])$. This approach is used to simplify the proof of the self-normalized Donsker theorem in Csörgő et al. (2003). Some notes on spheres with respect to $\ell _{p}$-norms are given.

The self-normalized Donsker theorem revisited

Peter Parczewski

https://doi.org/10.15559/17-MSTA82

Pub. online: 18 Sep 2017 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 4, Issue 3 (2017), pp. 189–198

Abstract

Editorial

K. Kubilius Yu. Mishura L. Sakhno

https://doi.org/10.15559/17-VMSTA81

Pub. online: 3 Jul 2017 Type: Editorial

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 4, Issue 2 (2017), pp. 91–92

Editorial

K. Kubilius Yu. Mishura L. Sakhno

https://doi.org/10.15559/17-MSTA81

Pub. online: 3 Jul 2017 Type: Editorial

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 4, Issue 2 (2017), pp. 91–92

Compositions of Poisson and Gamma processes

Khrystyna Buchak Lyudmyla Sakhno

https://doi.org/10.15559/17-VMSTA79

Pub. online: 29 Jun 2017 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 4, Issue 2 (2017), pp. 161–188

Abstract

In the paper we study the models of time-changed Poisson and Skellam-type processes, where the role of time is played by compound Poisson-Gamma subordinators and their inverse (or first passage time) processes. We obtain explicitly the probability distributions of considered time-changed processes and discuss their properties.

Compositions of Poisson and Gamma processes

Khrystyna Buchak Lyudmyla Sakhno

https://doi.org/10.15559/17-MSTA79

Pub. online: 29 Jun 2017 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 4, Issue 2 (2017), pp. 161–188

Abstract

Bonus–malus systems with different claim types and varying deductibles

Olena Ragulina

https://doi.org/10.15559/17-VMSTA80

Pub. online: 28 Jun 2017 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 4, Issue 2 (2017), pp. 141–159

Abstract

The paper deals with bonus–malus systems with different claim types and varying deductibles. The premium relativities are softened for the policyholders who are in the malus zone and these policyholders are subject to per claim deductibles depending on their levels in the bonus–malus scale and the types of the reported claims. We introduce such bonus–malus systems and study their basic properties. In particular, we investigate when it is possible to introduce varying deductibles, what restrictions we have and how we can do this. Moreover, we deal with the special case where varying deductibles are applied to the claims reported by policyholders occupying the highest level in the bonus–malus scale and consider two allocation principles for the deductibles. Finally, numerical illustrations are presented.

Bonus–malus systems with different claim types and varying deductibles

Olena Ragulina

https://doi.org/10.15559/17-MSTA80

Pub. online: 28 Jun 2017 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 4, Issue 2 (2017), pp. 141–159

Abstract

Multi-state models for evaluating conversion options in life insurance

Guglielmo D’Amico

Montserrat Guillen Raimondo Manca Filippo Petroni

https://doi.org/10.15559/17-VMSTA78

Pub. online: 10 May 2017 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 4, Issue 2 (2017), pp. 127–139

Abstract

In this paper we propose a multi-state model for the evaluation of the conversion option contract. The multi-state model is based on age-indexed semi-Markov chains that are able to reproduce many important aspects that influence the valuation of the option such as the duration problem, the time non-homogeneity and the ageing effect. The value of the conversion option is evaluated after the formal description of this contract.

Multi-state models for evaluating conversion options in life insurance

Guglielmo D’Amico

Montserrat Guillen Raimondo Manca Filippo Petroni

https://doi.org/10.15559/17-MSTA78

Pub. online: 10 May 2017 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 4, Issue 2 (2017), pp. 127–139

Abstract

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