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Practical approaches to the estimation of the ruin probability in a risk model with additional funds

Yuliya Mishura Olena Ragulina Oleksandr Stroyev

https://doi.org/10.15559/15-VMSTA18

Pub. online: 2 Feb 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 1, Issue 2 (2014), pp. 167–180

Abstract

We deal with a generalization of the classical risk model when an insurance company gets additional funds whenever a claim arrives and consider some practical approaches to the estimation of the ruin probability. In particular, we get an upper exponential bound and construct an analogue to the De Vylder approximation for the ruin probability. We compare results of these approaches with statistical estimates obtained by the Monte Carlo method for selected distributions of claim sizes and additional funds.

Practical approaches to the estimation of the ruin probability in a risk model with additional funds

Yuliya Mishura Olena Ragulina Oleksandr Stroyev

https://doi.org/10.15559/15-MSTA18

Pub. online: 2 Feb 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 1, Issue 2 (2014), pp. 167–180

Abstract

A martingale bound for the entropy associated with a trimmed filtration on

R^{d}

Alexei Kulik Taras Tymoshkevych

https://doi.org/10.15559/15-VMSTA16

Pub. online: 2 Feb 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 1, Issue 2 (2014), pp. 151–165

Abstract

Using martingale methods, we provide bounds for the entropy of a probability measure on ${\mathbb{R}}^{d}$ with the right-hand side given in a certain integral form. As a corollary, in the one-dimensional case, we obtain a weighted log-Sobolev inequality.

A martingale bound for the entropy associated with a trimmed filtration on

R^{d}

Alexei Kulik Taras Tymoshkevych

https://doi.org/10.15559/15-MSTA16

Pub. online: 2 Feb 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 1, Issue 2 (2014), pp. 151–165

Abstract

A criterion for testing hypotheses about the covariance function of a stationary Gaussian stochastic process

Yuriy Kozachenko Viktor Troshki

https://doi.org/10.15559/15-VMSTA17

Pub. online: 29 Jan 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 1, Issue 2 (2014), pp. 139–149

Abstract

We consider a measurable stationary Gaussian stochastic process. A criterion for testing hypotheses about the covariance function of such a process using estimates for its norm in the space $L_{p}(\mathbb{T})$, $p\ge 1$, is constructed.

A criterion for testing hypotheses about the covariance function of a stationary Gaussian stochastic process

Yuriy Kozachenko Viktor Troshki

https://doi.org/10.15559/15-MSTA17

Pub. online: 29 Jan 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 1, Issue 2 (2014), pp. 139–149

Abstract

Heat equation with general stochastic measure colored in time

Vadym Radchenko

https://doi.org/10.15559/14-VMSTA14

Pub. online: 5 Dec 2014 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 1, Issue 2 (2014), pp. 129–138

Abstract

A stochastic heat equation on $[0,T]\times \mathbb{R}$ driven by a general stochastic measure $d\mu (t)$ is investigated in this paper. For the integrator μ, we assume the σ-additivity in probability only. The existence, uniqueness, and Hölder regularity of the solution are proved.

Heat equation with general stochastic measure colored in time