A. Grigutis

activity

20162026

most citedRuin probability in the three-seasonal discrete-time risk model

9 citations · 32 across the 18 of their papers we have counts for

collaborators

19 papers

math.NT2026

Four explicit continued fractions for values of the Lerch transcendent and the Hurwitz zeta function

Andrius Grigutis, Yuri Matiyasevich, Lukas Turčinskas

We prove four explicit continued fraction representations for the Lerch transcendent $Φ (z, s, M + 1)$ , where $ℜ M > 0$ and $(z, s) \in {(- 1, 1), (- 1, 2), (1, 2), (1, 3)}$ . All of the continu…

hep-th2026

Real-time thermal self-energies: In the variational bases and spaces

M. A. A. Ahmed, H. Zainuddin, N. M. Shah

In this work, we introduce a systematic study for studying the scalar propagator and tadpole self-energy by considering an arbitrary parameter $σ$ that allows for a path integral d…

math.PR2026

The limit law of the maximum of discrete partial-sums distribution II

Andrius Grigutis, Juozas Petkelis

Let $X_{1}, X_{2}, \dots, X_{N}$ , $N \in N$ be independent, discrete, integer-valued random variables. Assume that $X_{j} ⩾ m_{j}$ almost surely for each $j=1,\,2,\,\ldots,\…

math.PR2026

Several expressions of the net single premiums under the constant force of mortality

Andrius Grigutis, Laurynas Lukoševičius, Mindaugas Venckevičius

In this article, we present several formulas that make it easier to compute the net single premiums when the mortality force over the fractional ages is assumed to be constant (C).…

math.NT2025★ 1 cited

Note on the positivity of the real part of the log-derivative of the Riemann $ξ$ -function near the critical line

Andrius Grigutis, Lukas Turčinskas

In this work, we investigate the positivity of the real part of the log-derivative of the Riemann $ξ$ -function in the region $1/2 + 1/ lo g t < σ < 1$ , where $t$ is sufficiently la…

math.NT2025

Picturesque convolution-like recurrences and partial sums' generation

Ignas Gasparavičius, Andrius Grigutis, Juozas Petkelis

Let $b = {b_{0}, b_{1}, \dots}$ be the known sequence of numbers such that $b_{0} \neq = 0$ . In this work, we develop methods to find another sequence ${\pmb a}=\{a_0,\,a_1,\,\ldot…

math.PR2025

Several facts about Theodor Wittstein, Gaetano Balducci, and some expressions of the net single premiums under their mortality assumption

Andrius Grigutis, Eglė Matulevičiūtė, Mindaugas Venckevičius

The mathematical essence in life insurance spins around the search of the nu\-me\-ri\-cal characteristics of the random variables $T_{x}$ , $ν^{T_{x}}$ , $T_{x} ν^{T_{x}}$ , etc., where $ν$ (d…

math.PR2024

The limit law of certain discrete multivariate distributions

Andrius Grigutis, Artur Nakliuda

Let $X_{1}, X_{2}, \dots, X_{N}$ , $N \in N$ be independent but not necessarily identically distributed discrete and integer-valued random variables. Assume that $X_1\geqslant…

econ.GN2024★ 1 cited

The Famous American Economist H. Markowitz and Mathematical Overview of his Portfolio Selection Theory

Ignas Gasparavičius, Andrius Grigutis

This survey article is dedicated to the life of the famous American economist H. Markowitz (1927--2023). We do revisit the main statements of the portfolio selection theory in term…

math.PR2023★ 3 cited

On the exact survival probability by setting discrete random variables in E. Sparre Andersen's model

Andrius Grigutis

In this work, we propose a simplification of the Pollaczek-Khinchine formula for the ultimate time survival (or ruin) probability calculation in exchange for a few assumptions on t…

math.PR2023★ 4 cited

Ruin probability for renewal risk models with neutral net profit condition

Andrius Grigutis, Arvydas Karbonskis, Jonas Šiaulys

In ruin theory, the net profit condition intuitively means that the incurred random claims on average do not occur more often than premiums are gained. The breach of the net profit…

q-fin.RM2023★ 1 cited

Probabilistic Overview of Probabilities of Default for Low Default Portfolios by K. Pluto and D. Tasche

Andrius Grigutis

This article gives a probabilistic overview of the widely used method of default probability estimation proposed by K. Pluto and D. Tasche. There are listed detailed assumptions an…

math.PR2022

Distribution of shifted discrete random walk generated by distinct random variables and applications in ruin theory

Simonas Gervė, Andrius Grigutis

In this paper, we set up the distribution function $φ (u) = P (n ⩾ 1 sup i = 1 \sum n (X_{i} - κ) < u),$ and the generating function of $φ (u + 1)$ ,…

math.PR2022★ 8 cited

Distribution of Shifted Discrete Random Walk and Vandermonde matrices

Andrius Grigutis

In this work we set up the generating function of the ultimate time survival probability $φ (u + 1)$ , where $$φ(u)=\mathbb{P}\left(\sup_{n\geqslant 1}\sum_{i=1}^{n}\left(X_i-κ\right)<…

math.PR2022★ 3 cited

Multi seasonal discrete time risk model revisited

Andrius Grigutis, Jonas Jankauskas, Jonas Šiaulys

In this work we set up the distribution function of $M := sup_{n ⩾ 1} \sum_{i = 1}^{n} (Z_{i} - 1)$ , where the random walk $\sum_{i = 1}^{n} Z_{i}, n \in N,$ is generate…

math.NT2022★ 2 cited

On a positivity property of the real part of logarithmic derivative of the Riemann $ξ$ -function

Edvinas Goldštein, Andrius Grigutis

In this paper we investigate the positivity property of the real part of logarithmic derivative of the Riemann $ξ$ -function for $1/2 < σ < 1$ and sufficiently large $t$ . We give an exp…

math.PR2021

Bi-seasonal discrete time risk model with income rate two

Alina Alencenovič, Andrius Grigutis

This paper proceeds an approximate calculation of ultimate time survival probability for bi-seasonal discrete time risk model when premium rate equals two. The same model with inco…

math.PR2021

On $2 \times 2$ determinants originating from survival probabilities in homogeneous discrete time risk model

Andrius Grigutis, Jonas Jankauskas

We analyze $2 \times 2$ Hankel-like determinants $D_{n}$ that arise in the initial values problem for the ultimate time survival probability $φ (u)$ in a homogeneous discrete time risk…

math.PR2016★ 9 cited

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

Andrius Grigutis, Agneška Korvel, Jonas Šiaulys

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 distri…

Four explicit continued fractions for values of the Lerch transcendent and the Hurwitz zeta function

Real-time thermal self-energies: In the variational bases and spaces

The limit law of the maximum of discrete partial-sums distribution II

Several expressions of the net single premiums under the constant force of mortality

Note on the positivity of the real part of the log-derivative of the Riemann ξ-function near the critical line

Picturesque convolution-like recurrences and partial sums' generation

Several facts about Theodor Wittstein, Gaetano Balducci, and some expressions of the net single premiums under their mortality assumption

The limit law of certain discrete multivariate distributions

The Famous American Economist H. Markowitz and Mathematical Overview of his Portfolio Selection Theory

On the exact survival probability by setting discrete random variables in E. Sparre Andersen's model

Ruin probability for renewal risk models with neutral net profit condition

Probabilistic Overview of Probabilities of Default for Low Default Portfolios by K. Pluto and D. Tasche

Distribution of shifted discrete random walk generated by distinct random variables and applications in ruin theory

Distribution of Shifted Discrete Random Walk and Vandermonde matrices

Multi seasonal discrete time risk model revisited

On a positivity property of the real part of logarithmic derivative of the Riemann ξ-function

Bi-seasonal discrete time risk model with income rate two

On 2×2 determinants originating from survival probabilities in homogeneous discrete time risk model

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

Note on the positivity of the real part of the log-derivative of the Riemann $ξ$ -function near the critical line

On a positivity property of the real part of logarithmic derivative of the Riemann $ξ$ -function

On $2 \times 2$ determinants originating from survival probabilities in homogeneous discrete time risk model