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Subject index

https://doi.org/10.15559/15-VMSTA24SI

Pub. online: 31 Dec 2015 Type: Subject Index

Journal: Modern Stochastics: Theory and Applications Volume 2, Issue 4 (2015), pp. 445–446

Subject index

https://doi.org/10.15559/15-MSTA24SI

Pub. online: 31 Dec 2015 Type: Subject Index

Journal: Modern Stochastics: Theory and Applications* Volume 2, Issue 4 (2015), pp. 445–446

Author index

https://doi.org/10.15559/15-VMSTA24AI

Pub. online: 31 Dec 2015 Type: Author Index

Journal: Modern Stochastics: Theory and Applications Volume 2, Issue 4 (2015), p. 443

Author index

https://doi.org/10.15559/15-MSTA24AI

Pub. online: 31 Dec 2015 Type: Author Index

Journal: Modern Stochastics: Theory and Applications* Volume 2, Issue 4 (2015), p. 443

Ruin probability in the three-seasonal discrete-time risk model

Andrius Grigutis Agneška Korvel Jonas Šiaulys

https://doi.org/10.15559/15-VMSTA45

Pub. online: 30 Dec 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 2, Issue 4 (2015), pp. 421–441

Abstract

This paper deals with the discrete-time risk model with nonidentically distributed claims. We suppose that the claims repeat with time periods of three units, that is, claim distributions coincide at times $\{1,4,7,\dots \}$, at times $\{2,5,8,\dots \}$, and at times $\{3,6,9,\dots \}$. We present the recursive formulas to calculate the finite-time and ultimate ruin probabilities. We illustrate the theoretical results by several numerical examples.

Ruin probability in the three-seasonal discrete-time risk model

Andrius Grigutis Agneška Korvel Jonas Šiaulys

https://doi.org/10.15559/15-MSTA45

Pub. online: 30 Dec 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 2, Issue 4 (2015), pp. 421–441

Abstract

Accuracy of discrete approximation for integral functionals of Markov processes

Iurii Ganychenko Victoria Knopova Alexei Kulik

https://doi.org/10.15559/15-VMSTA46

Pub. online: 30 Dec 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 2, Issue 4 (2015), pp. 401–420

Abstract

The article is devoted to the estimation of the convergence rate of integral functionals of a Markov process. Under the assumption that the given Markov process admits a transition probability density differentiable in t and the derivative has an integrable upper bound of a certain type, we derive the accuracy rates for strong and weak approximations of the functionals by Riemannian sums. We also develop a version of the parametrix method, which provides the required upper bound for the derivative of the transition probability density for a solution of an SDE driven by a locally stable process. As an application, we give accuracy bounds for an approximation of the price of an occupation time option.

Accuracy of discrete approximation for integral functionals of Markov processes

Iurii Ganychenko Victoria Knopova Alexei Kulik

https://doi.org/10.15559/15-MSTA46

Pub. online: 30 Dec 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 2, Issue 4 (2015), pp. 401–420

Abstract

Distance between exact and approximate distributions of partial maxima under power normalization

Attahalli Shivanarayanaprasad Praveena Sreenivasan Ravi

https://doi.org/10.15559/15-VMSTA42

Pub. online: 23 Dec 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 2, Issue 4 (2015), pp. 391–399

Abstract

We obtain the distance between the exact and approximate distributions of partial maxima of a random sample under power normalization. It is observed that the Hellinger distance and variational distance between the exact and approximate distributions of partial maxima under power normalization is the same as the corresponding distances under linear normalization.

Distance between exact and approximate distributions of partial maxima under power normalization

Attahalli Shivanarayanaprasad Praveena Sreenivasan Ravi

https://doi.org/10.15559/15-MSTA42

Pub. online: 23 Dec 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 2, Issue 4 (2015), pp. 391–399

Abstract

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