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Probabilistic Models in Insurance and Finance

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A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Probability and Statistics".

Deadline for manuscript submissions: 31 August 2024 | Viewed by 5314

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Special Issue Editor

Prof. Dr. Jonas Šiaulys

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Guest Editor

Institute of Mathematics, Vilnius University, Naugarduko 24, LT-032225 Vilnius, Lithuania
Interests: stochastic processes; ruin theory; actuarial mathematics; heavy tails
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Special Issue Information

Dear Colleagues,

Probability theory together with mathematical statistics are very important mathematical tools for studying various processes in nature and society where the behavior of underlying observed phenomena is driven by randomness. This approach, where deterministic description is inefficient and should be replaced by stochastic models, is often used in insurance, finance, physics, chemistry, medicine, and many other fields. In insurance and finance, stochastic models are widely used for the forecasting of future states. First of all, the insurance and financial business raises specific questions related to extreme value theory, time-series analysis, heavy-tailed distributions, survival analysis, premium calculation principles, risk measures analysis, ruin probabilities estimation, etc.

The purpose of this Special Issue is to gather a collection of articles reflecting the latest developments in insurance and finance of applied probability, such as long memory processes in finance, risk renewal processes in insurance, risks measures in insurance and finance, the properties of heavy-tailed distributions, conditional heteroscedasticity, extreme value theory, the properties of survival functions, and others.

Prof. Dr. Jonas Šiaulys
Guest Editor

Manuscript Submission Information

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Keywords

stochastic models for insurance
stochastic models for finance
survival functions
long memory
financial time series
risk measures
ruin probabilities
heavy-tailed distributions
transformation of distributions
asymptotic estimates

Published Papers (5 papers)

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Research

Jump to: Review

12 pages, 317 KiB

Open AccessArticle

Scale Mixture of Gleser Distribution with an Application to Insurance Data

by Neveka M. Olmos, Emilio Gómez-Déniz and Osvaldo Venegas

Mathematics 2024, 12(9), 1397; https://doi.org/10.3390/math12091397 - 3 May 2024

Viewed by 369

Abstract

In this paper, the scale mixture of the Gleser (SMG) distribution is introduced. This new distribution is the product of a scale mixture between the Gleser (G) distribution and the Beta

(a, 1)

distribution. The SMG distribution is an alternative [...] Read more.

In this paper, the scale mixture of the Gleser (SMG) distribution is introduced. This new distribution is the product of a scale mixture between the Gleser (G) distribution and the Beta

(a, 1)

distribution. The SMG distribution is an alternative to distributions with two parameters and a heavy right tail. We study its representation and some basic properties, maximum likelihood inference, and Fisher’s information matrix. We present an application to a real dataset in which the SMG distribution shows a better fit than two other known distributions. Full article

(This article belongs to the Special Issue Probabilistic Models in Insurance and Finance)

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15 pages, 320 KiB

Open AccessArticle

Truncated Moments for Heavy-Tailed and Related Distribution Classes

by Saulius Paukštys, Jonas Šiaulys and Remigijus Leipus

Mathematics 2023, 11(9), 2172; https://doi.org/10.3390/math11092172 - 5 May 2023

Cited by 1 | Viewed by 961

Abstract

Suppose that

ξ^{+}

is the positive part of a random variable defined on the probability space

(Ω, F, P)

with the distribution function

F_{ξ}

. When the moment

E {(ξ^{+})}^{p}

of order

p > 0

[...] Read more.

Suppose that

ξ^{+}

is the positive part of a random variable defined on the probability space

(Ω, F, P)

with the distribution function

F_{ξ}

. When the moment

E {(ξ^{+})}^{p}

of order

p > 0

is finite, then the truncated moment

{\bar{F}}_{ξ, p} (x) = min \{1, E (ξ^{p} 1 I_{{ξ > x}})\}

, defined for all

x ⩾ 0

, is the survival function or, in other words, the distribution tail of the distribution function

F_{ξ, p}

. In this paper, we examine which regularity properties transfer from the distribution function

F_{ξ}

to the distribution function

F_{ξ, p}

and which properties transfer from the function

F_{ξ, p}

to the function

F_{ξ}

. The construction of the distribution function

F_{ξ, p}

describes the truncated moment transformation of the initial distribution function

F_{ξ}

. Our results show that the subclasses of heavy-tailed distributions, such as regularly varying, dominatedly varying, consistently varying and long-tailed distribution classes, are closed under this truncated moment transformation. We also show that exponential-like-tailed and generalized long-tailed distribution classes, which contain both heavy- and light-tailed distributions, are also closed under the truncated moment transformation. On the other hand, we demonstrate that regularly varying and exponential-like-tailed distribution classes also admit inverse transformation closures, i.e., from the condition that

F_{ξ, p}

belongs to one of these classes, it follows that

F_{ξ}

also belongs to the corresponding class. In general, the obtained results complement the known closure properties of distribution regularity classes. Full article

(This article belongs to the Special Issue Probabilistic Models in Insurance and Finance)

31 pages, 5172 KiB

Open AccessArticle

A Novel Model for Quantitative Risk Assessment under Claim-Size Data with Bimodal and Symmetric Data Modeling

by Haitham M. Yousof, Walid Emam, Yusra Tashkandy, M. Masoom Ali, R. Minkah and Mohamed Ibrahim

Mathematics 2023, 11(6), 1284; https://doi.org/10.3390/math11061284 - 7 Mar 2023

Cited by 6 | Viewed by 982

Abstract

A novel flexible extension of the Chen distribution is defined and studied in this paper. Relevant statistical properties of the novel model are derived. For the actuarial risk analysis and evaluation, the maximum likelihood, weighted least squares, ordinary least squares, Cramer–von Mises, moments, and Anderson–Darling methods are utilized. For actuarial purposes, a comprehensive simulation study is presented using various combinations to evaluate the performance of the six methods in analyzing insurance risks. These six methods are used in evaluating actuarial risks using insurance claims data. Two applications on bimodal data are presented to highlight the flexibility and relevance of the new distribution. The new distribution is compared to several competing distributions. Actuarial risks are analyzed and evaluated using actuarial data, and the ability to disclose actuarial risks is compared by a comprehensive simulation study, through which actuarial disclosure models are compared using a wide range of well-known models. Full article

(This article belongs to the Special Issue Probabilistic Models in Insurance and Finance)

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11 pages, 790 KiB

Open AccessArticle

Product Convolution of Generalized Subexponential Distributions

by Gustas Mikutavičius and Jonas Šiaulys

Mathematics 2023, 11(1), 248; https://doi.org/10.3390/math11010248 - 3 Jan 2023

Cited by 3 | Viewed by 1067

Abstract

Assume that

ξ

and

η

are two independent random variables with distribution functions

F_{ξ}

and

F_{η}

, respectively. The distribution of a random variable

ξ η

, denoted by

F_{ξ} \otimes F_{η}

, is called the product-convolution of [...] Read more.

Assume that

ξ

and

η

are two independent random variables with distribution functions

F_{ξ}

and

F_{η}

, respectively. The distribution of a random variable

ξ η

, denoted by

F_{ξ} \otimes F_{η}

, is called the product-convolution of

F_{ξ}

and

F_{η}

. It is proved that

F_{ξ} \otimes F_{η}

is a generalized subexponential distribution if

F_{ξ}

belongs to the class of generalized subexponential distributions and

η

is nonnegative and not degenerated at zero. Full article

(This article belongs to the Special Issue Probabilistic Models in Insurance and Finance)

Review

Jump to: Research

35 pages, 968 KiB

Open AccessReview

From Constant to Rough: A Survey of Continuous Volatility Modeling

by Giulia Di Nunno, Kęstutis Kubilius, Yuliya Mishura and Anton Yurchenko-Tytarenko

Mathematics 2023, 11(19), 4201; https://doi.org/10.3390/math11194201 - 8 Oct 2023

Cited by 1 | Viewed by 1427

Abstract

In this paper, we present a comprehensive survey of continuous stochastic volatility models, discussing their historical development and the key stylized facts that have driven the field. Special attention is dedicated to fractional and rough methods: without advocating for either roughness or long memory, we outline the motivation behind them and characterize some landmark models. In addition, we briefly touch on the problem of VIX modeling and recent advances in the SPX-VIX joint calibration puzzle. Full article

(This article belongs to the Special Issue Probabilistic Models in Insurance and Finance)

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