Editorial

7 pages, 312 KiB

Open AccessEditorial

Special Issue “Risk, Ruin and Survival: Decision Making in Insurance and Finance”

by Jiandong Ren, Kristina Sendova and Ričardas Zitikis

Risks 2019, 7(3), 96; https://doi.org/10.3390/risks7030096 - 07 Sep 2019

Cited by 2 | Viewed by 2945

It has been six years since Editor-in-Chief Steffensen (2013) wrote in his editorial that “to Risks inclusiveness, inter-disciplinarity, and open-mindedness is the very starting point [...] Full article

(This article belongs to the Special Issue Risk, Ruin and Survival: Decision Making in Insurance and Finance)

Research

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26 pages, 512 KiB

Open AccessArticle

Spatial Risk Measures and Rate of Spatial Diversification

by Erwan Koch

Risks 2019, 7(2), 52; https://doi.org/10.3390/risks7020052 - 02 May 2019

Cited by 3 | Viewed by 2994

Abstract

An accurate assessment of the risk of extreme environmental events is of great importance for populations, authorities and the banking/insurance/reinsurance industry. Koch (2017) introduced a notion of spatial risk measure and a corresponding set of axioms which are well suited to analyze the [...] Read more.

An accurate assessment of the risk of extreme environmental events is of great importance for populations, authorities and the banking/insurance/reinsurance industry. Koch (2017) introduced a notion of spatial risk measure and a corresponding set of axioms which are well suited to analyze the risk due to events having a spatial extent, precisely such as environmental phenomena. The axiom of asymptotic spatial homogeneity is of particular interest since it allows one to quantify the rate of spatial diversification when the region under consideration becomes large. In this paper, we first investigate the general concepts of spatial risk measures and corresponding axioms further and thoroughly explain the usefulness of this theory for both actuarial science and practice. Second, in the case of a general cost field, we give sufficient conditions such that spatial risk measures associated with expectation, variance, value-at-risk as well as expected shortfall and induced by this cost field satisfy the axioms of asymptotic spatial homogeneity of order 0, −2, −1 and −1, respectively. Last but not least, in the case where the cost field is a function of a max-stable random field, we provide conditions on both the function and the max-stable field ensuring the latter properties. Max-stable random fields are relevant when assessing the risk of extreme events since they appear as a natural extension of multivariate extreme-value theory to the level of random fields. Overall, this paper improves our understanding of spatial risk measures as well as of their properties with respect to the space variable and generalizes many results obtained in Koch (2017). Full article

(This article belongs to the Special Issue Risk, Ruin and Survival: Decision Making in Insurance and Finance)

20 pages, 585 KiB

Open AccessArticle

Practice Oriented and Monte Carlo Based Estimation of the Value-at-Risk for Operational Risk Measurement

by Francesca Greselin, Fabio Piacenza and Ričardas Zitikis

Risks 2019, 7(2), 50; https://doi.org/10.3390/risks7020050 - 01 May 2019

Cited by 4 | Viewed by 3810

Abstract

We explore the Monte Carlo steps required to reduce the sampling error of the estimated 99.9% quantile within an acceptable threshold. Our research is of primary interest to practitioners working in the area of operational risk measurement, where the annual loss distribution cannot [...] Read more.

We explore the Monte Carlo steps required to reduce the sampling error of the estimated 99.9% quantile within an acceptable threshold. Our research is of primary interest to practitioners working in the area of operational risk measurement, where the annual loss distribution cannot be analytically determined in advance. Usually, the frequency and the severity distributions should be adequately combined and elaborated with Monte Carlo methods, in order to estimate the loss distributions and risk measures. Naturally, financial analysts and regulators are interested in mitigating sampling errors, as prescribed in EU Regulation 2018/959. In particular, the sampling error of the 99.9% quantile is of paramount importance, along the lines of EU Regulation 575/2013. The Monte Carlo error for the operational risk measure is here assessed on the basis of the binomial distribution. Our approach is then applied to realistic simulated data, yielding a comparable precision of the estimate with a much lower computational effort, when compared to bootstrap, Monte Carlo repetition, and two other methods based on numerical optimization. Full article

(This article belongs to the Special Issue Risk, Ruin and Survival: Decision Making in Insurance and Finance)

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27 pages, 1386 KiB

Open AccessArticle

National Culture and Corporate Rating Migrations

by Huong Dieu Dang

Risks 2018, 6(4), 130; https://doi.org/10.3390/risks6040130 - 14 Nov 2018

Cited by 4 | Viewed by 3749

Abstract

The informal constraints that arise from the national culture in which a firm resides have a pervasive impact on managerial decision making and corporate credit risk, which in turn impacts on corporate ratings and rating changes. In some cultures, firms are naturally predisposed [...] Read more.

The informal constraints that arise from the national culture in which a firm resides have a pervasive impact on managerial decision making and corporate credit risk, which in turn impacts on corporate ratings and rating changes. In some cultures, firms are naturally predisposed to rating changes in a particular direction (downgrade or upgrade) while, in other cultures, firms are more likely to migrate from the current rating in either direction. This study employs a survival analysis framework to examine the effect of national culture on the probability of rating transitions of 5360 firms across 50 countries over the period 1985–2010. Firms located in long-term oriented cultures are less likely to be downgraded and, in some cases, more likely to be upgraded. Downgrades occur more often in strong uncertainty-avoiding countries and less often in large power distance (hierarchy) and embeddedness countries. There is some evidence that masculinity predisposes firms to more rating transitions. Studying culture helps enrich our understanding of corporate rating migrations, and helps develop predictive models of corporate rating changes across countries. Full article

(This article belongs to the Special Issue Risk, Ruin and Survival: Decision Making in Insurance and Finance)

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26 pages, 3586 KiB

Open AccessArticle

A Maximal Tail Dependence-Based Clustering Procedure for Financial Time Series and Its Applications in Portfolio Selection

by Xin Liu, Jiang Wu, Chen Yang and Wenjun Jiang

Risks 2018, 6(4), 115; https://doi.org/10.3390/risks6040115 - 09 Oct 2018

Cited by 7 | Viewed by 3320

Abstract

In this paper, we propose a clustering procedure of financial time series according to the coefficient of weak lower-tail maximal dependence (WLTMD). Due to the potential asymmetry of the matrix of WLTMD coefficients, the clustering procedure is based on a generalized weighted cuts [...] Read more.

In this paper, we propose a clustering procedure of financial time series according to the coefficient of weak lower-tail maximal dependence (WLTMD). Due to the potential asymmetry of the matrix of WLTMD coefficients, the clustering procedure is based on a generalized weighted cuts method instead of the dissimilarity-based methods. The performance of the new clustering procedure is evaluated by simulation studies. Finally, we illustrate that the optimal mean-variance portfolio constructed based on the resulting clusters manages to reduce the risk of simultaneous large losses effectively. Full article

(This article belongs to the Special Issue Risk, Ruin and Survival: Decision Making in Insurance and Finance)

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13 pages, 1079 KiB

Open AccessArticle

Numerical Ruin Probability in the Dual Risk Model with Risk-Free Investments

by Sooie-Hoe Loke and Enrique Thomann

Risks 2018, 6(4), 110; https://doi.org/10.3390/risks6040110 - 01 Oct 2018

Cited by 4 | Viewed by 2886

Abstract

In this paper, a dual risk model under constant force of interest is considered. The ruin probability in this model is shown to satisfy an integro-differential equation, which can then be written as an integral equation. Using the collocation method, the ruin probability [...] Read more.

In this paper, a dual risk model under constant force of interest is considered. The ruin probability in this model is shown to satisfy an integro-differential equation, which can then be written as an integral equation. Using the collocation method, the ruin probability can be well approximated for any gain distributions. Examples involving exponential, uniform, Pareto and discrete gains are considered. Finally, the same numerical method is applied to the Laplace transform of the time of ruin. Full article

(This article belongs to the Special Issue Risk, Ruin and Survival: Decision Making in Insurance and Finance)

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11 pages, 765 KiB

Open AccessArticle

A User-Friendly Algorithm for Detecting the Influence of Background Risks on a Model

by Nadezhda Gribkova and Ričardas Zitikis

Risks 2018, 6(3), 100; https://doi.org/10.3390/risks6030100 - 14 Sep 2018

Cited by 5 | Viewed by 3044

Abstract

Background, or systematic, risks are integral parts of many systems and models in insurance and finance. These risks can, for example, be economic in nature, or they can carry more technical connotations, such as errors or intrusions, which could be intentional or unintentional. [...] Read more.

Background, or systematic, risks are integral parts of many systems and models in insurance and finance. These risks can, for example, be economic in nature, or they can carry more technical connotations, such as errors or intrusions, which could be intentional or unintentional. A most natural question arises from the practical point of view: is the given system really affected by these risks? In this paper we offer an algorithm for answering this question, given input-output data and appropriately constructed statistics, which rely on the order statistics of inputs and the concomitants of outputs. Even though the idea is rooted in complex statistical and probabilistic considerations, the algorithm is easy to implement and use in practice, as illustrated using simulated data. Full article

(This article belongs to the Special Issue Risk, Ruin and Survival: Decision Making in Insurance and Finance)

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17 pages, 1018 KiB

Open AccessArticle

Moments of Compound Renewal Sums with Dependent Risks Using Mixing Exponential Models

by Fouad Marri, Franck Adékambi and Khouzeima Moutanabbir

Risks 2018, 6(3), 86; https://doi.org/10.3390/risks6030086 - 24 Aug 2018

Cited by 4 | Viewed by 3094

Abstract

In this paper, we study the discounted renewal aggregate claims with a full dependence structure. Based on a mixing exponential model, the dependence among the inter-claim times, the claim sizes, as well as the dependence between the inter-claim times and the claim sizes [...] Read more.

In this paper, we study the discounted renewal aggregate claims with a full dependence structure. Based on a mixing exponential model, the dependence among the inter-claim times, the claim sizes, as well as the dependence between the inter-claim times and the claim sizes are included. The main contribution of this paper is the derivation of the closed-form expressions for the higher moments of the discounted aggregate renewal claims. Then, explicit expressions of these moments are provided for specific copulas families and some numerical illustrations are given to analyze the impact of dependency on the moments of the discounted aggregate amount of claims. Full article

(This article belongs to the Special Issue Risk, Ruin and Survival: Decision Making in Insurance and Finance)

11 pages, 859 KiB

Open AccessArticle

A VaR-Type Risk Measure Derived from Cumulative Parisian Ruin for the Classical Risk Model

by Mohamed Amine Lkabous and Jean-François Renaud

Risks 2018, 6(3), 85; https://doi.org/10.3390/risks6030085 - 24 Aug 2018

Cited by 6 | Viewed by 3240

Abstract

In this short paper, we study a VaR-type risk measure introduced by Guérin and Renaud and which is based on cumulative Parisian ruin. We derive some properties of this risk measure and we compare it to the risk measures of Trufin et al. [...] Read more.

In this short paper, we study a VaR-type risk measure introduced by Guérin and Renaud and which is based on cumulative Parisian ruin. We derive some properties of this risk measure and we compare it to the risk measures of Trufin et al. and Loisel and Trufin. Full article

(This article belongs to the Special Issue Risk, Ruin and Survival: Decision Making in Insurance and Finance)

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20 pages, 1544 KiB

Open AccessArticle

On a Multiplicative Multivariate Gamma Distribution with Applications in Insurance

by Vadim Semenikhine, Edward Furman and Jianxi Su

Risks 2018, 6(3), 79; https://doi.org/10.3390/risks6030079 - 12 Aug 2018

Cited by 9 | Viewed by 3940

Abstract

One way to formulate a multivariate probability distribution with dependent univariate margins distributed gamma is by using the closure under convolutions property. This direction yields an additive background risk model, and it has been very well-studied. An alternative way to accomplish the same [...] Read more.

One way to formulate a multivariate probability distribution with dependent univariate margins distributed gamma is by using the closure under convolutions property. This direction yields an additive background risk model, and it has been very well-studied. An alternative way to accomplish the same task is via an application of the Bernstein–Widder theorem with respect to a shifted inverse Beta probability density function. This way, which leads to an arguably equally popular multiplicative background risk model (MBRM), has been by far less investigated. In this paper, we reintroduce the multiplicative multivariate gamma (MMG) distribution in the most general form, and we explore its various properties thoroughly. Specifically, we study the links to the MBRM, employ the machinery of divided differences to derive the distribution of the aggregate risk random variable explicitly, look into the corresponding copula function and the measures of nonlinear correlation associated with it, and, last but not least, determine the measures of maximal tail dependence. Our main message is that the MMG distribution is (1) very intuitive and easy to communicate, (2) remarkably tractable, and (3) possesses rich dependence and tail dependence characteristics. Hence, the MMG distribution should be given serious considerations when modelling dependent risks. Full article

(This article belongs to the Special Issue Risk, Ruin and Survival: Decision Making in Insurance and Finance)

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16 pages, 440 KiB

Open AccessArticle

On the Moments and the Distribution of Aggregate Discounted Claims in a Markovian Environment

by Shuanming Li and Yi Lu

Risks 2018, 6(2), 59; https://doi.org/10.3390/risks6020059 - 23 May 2018

Cited by 2 | Viewed by 3078

Abstract

This paper studies the moments and the distribution of the aggregate discounted claims (ADCs) in a Markovian environment, where the claim arrivals, claim amounts, and forces of interest (for discounting) are influenced by an underlying Markov process. Specifically, we assume that claims occur [...] Read more.

This paper studies the moments and the distribution of the aggregate discounted claims (ADCs) in a Markovian environment, where the claim arrivals, claim amounts, and forces of interest (for discounting) are influenced by an underlying Markov process. Specifically, we assume that claims occur according to a Markovian arrival process (MAP). The paper shows that the vector of joint Laplace transforms of the ADC occurring in each state of the environment process by any specific time satisfies a matrix-form first-order partial differential equation, through which a recursive formula is derived for the moments of the ADC occurring in certain states (a subset). We also study two types of covariances of the ADC occurring in any two subsets of the state space and with two different time lengths. The distribution of the ADC occurring in certain states by any specific time is also investigated. Numerical results are also presented for a two-state Markov-modulated model case. Full article

(This article belongs to the Special Issue Risk, Ruin and Survival: Decision Making in Insurance and Finance)

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