arXiv subjects

Dimitrios G. Konstantinides

Publications and source records attributed to Dimitrios G. Konstantinides.

At least 19 recordsLinked to original sources

arXiv2026

Local uniform asymptotics for a non-standard risk model and interplay of insurance and financial risks stemming by systemic factors

In this paper we study local uniform, with respect to time, asymptotic expressions for the asymptotic behavior of the entrance probability of discounted aggregate claims to some rare sets, in a multivariate risk model with arbitrarily dependent insurance and financial risks. Our model is based on a multivariate version of a model, introduced by Guo (2022), and we consider that the logarithmic return process of the insurers investment portfolio is described by a jump-diffusion process. The dependence between the insurance and financial risks is implied by the dependence of the claim-vectors with the jumps of returns, and is arbitrary under some distributional conditions on the claim-vectors and the discounted claim-vectors. In opposite to previous papers on this topic, except the multidimensional extension, we consider that the model is driven by a common counting process, that is not necessarily renewal, the claim vectors are interdependent, and their distribution is not restricted to the class of (multivariate) regularly varying distributions. Under the condition that the claim vectors, and the discounted claim-vectors follows distributions from the class of multivariate consistently varying and positively decreasing distributions, and under some moment conditions on the jumps and the counting process, our main result shows the presence of multivariate linear single big jump principle of the discounted aggregate claims in this not necessarily Levy-Renewal environment. After restriction of the distributions to multivariate regular variation, we obtain more explicit expressions, under a slightly weaker moment condition on the jumps. We provide a corollary, in which the conditions of the main result are satisfied under a weak dependence structure and we find a more explicit asymptotic expression, using the technique of solution of the dependence.

math.PR↗

arXiv2026

Asymptotics of randomly weighted sums without moment conditions of random weights

In the paper, we investigate the asymptotics of randomly weighted sums with upper tail asymptotically independent and quasi-upper tail asymptotically independent primary random variables without requiring moment assumptions on random weights. For the case of primary random variables with regularly varying tails, we obtain more explicit results via an extension of Breiman's theorem. Then an application of the obtained results is established to asymptotically estimate for the finite-time and infinite-time ruin probabilities in a discrete-time risk model.

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arXiv2026

Asymptotics for aggregated interdependent multivariate subexponential claims with general investment returns

This paper investigates asymptotic estimates for the entrance probability of the discounted aggregate claim vector from a multivariate renewal risk model into some rare set. We provide asymptotic results for the entrance probability on both finite and infinite time horizons under various assumptions regarding the stochastic price process of the investment portfolio, the distribution class of claim vectors, and the dependence structure among the claim vectors. We note that the main results extend beyond the class of multivariate regular variation. Furthermore, we introduce two dependence structures to model the dependence among the claim vectors. In particular, our results are new even in the one-dimensional subcase.

math.PR↗

arXiv2026

Interplay of insurance and financial risks in a non Levy-Renewal environment

In this paper we consider a multivariate risk model, with common counting process and common process of logarithmic returns for the investment portfolio. We assume that the claim-vectors, the counting process and the logarithmic returns of the investment portfolio satisfy a weak dependence structure. Further, we consider that the counting process represents an inhomogeneous renewal process, and the logarithmic returns represent a cadlag process with independent but not necessarily stationary increments. Under these conditions we provide an asymptotic expression for the infinite-time entrance probability of the discounted aggregate claims into some rare set xA, where A denotes a set from a general set family, crucial for the actuarial practice, when the common distribution of the claim vectors belong to a multivariate heavy-tailed distribution class. This result, is derived under a moment condition for the financial risks, and underlines the multivariate linear single big jump principle. When we restrict the distribution class of the claim-vectors to multivariate regular variation, we find more explicit asymptotic expressions, weakening the moment conditions on the financial risks. The asymptotic formulas, derived through double dependence solution, become more direct and practical in applications. With respect to the technical part, due to non Levy-Renewal framework, the classical Kesten-Goldie theorems are not applicable, nor their extensions. The way we make the discretization of the process of the discounted aggregate claims permits to derive uniform asymptotics with respect to the number of summands, that facilitate the approximation of the infinite sums of the main results.

math.PR↗

arXiv2026

Random vectors in the presence of a single big jump

The multidimensional distributions with heavy tails attracted recently the attention of several papers on Applied Probability. However, the most of the works of the last decades are focused on multivariate regular variation, while the rest of the heavy-tailed distribution classes were not studied extensively. About the multivariate subexponentiality we can find several approximations, but none of them get established widely. Having in mind the single big jump and further the multivariate subexponentiality suggested by Samorodnitsky and Sun (2016), we introduce the multivariate long, dominatedly and constistently varying distribution classes. We examine the closure properties of these classes with respect to product convolution, to scale mixture and convolution of random vectors. Especially in the class of multivariate subexponential and dominatedly varying distributions we provide the asymptotic behavior of the random vector and its normalized Levy measure, through their linear combination, that leads to their characterization. Furthermore, we study the single big jump in finite and in random sums of random vectors, permitting some dependence structures, which contain the independence as special case. Finally, we present an application on the asymptotic evaluation of the present value of the total claims in a risk model, with common Poisson counting process, general financial factors and independent, identically distributed claims, with common multivariate subexponential distribution.

math.PR↗

arXiv2026

The Bivariate regular variation of randomly weighted sums revisited in the presence of interdependence

We study the joint distribution of two randomly weighted sums. Inspired by the practical applications, we assume that the main random variables follow the non-standard bivariate regular variation, symbolically BRV , to put emphasis to the value of inhomogeneity of the risk distribution tails, while the random weights are weakly dependent with main random variables. Under some moment conditions on the random weights we show that the randomly weighted sums have BRV distribution with an analytic relation for the Radon measure, that captures the interdependence between the random weights and the main random variables. Under some stronger moments conditions, our result is extended uniformly, with respect to summands, covering also the case of infinite randomly weighted sums. In order to keep weak dependence structure among the random weights and the main random variables, we require the random weights to be independent each other, something that does not happen in models with insurance and financial risks. Up to recent years, such kind of approximations, even in one-dimensional case, had mostly theoretical interest, since underline the presence of (multivariate linear) single big jump principle. However, here we provide an application of the main results on ruin probability in a new flexible credit risk model. In our model, although we restrict ourselves to standard BRV , the obliged do not enter - quit necessarily simultaneously to the system, while the breach probability is not necessarily independent of the the amount of breach for the obliged. Finally, in the nonstandard BRV , with asymptotically dependent risks, we provide an application of the main results, to find the asymptotic behavior of a risk measure, which is called joint expected shortfall, that plays crucial role to the measure of the contagion of extreme risks

math.PR↗

arXiv2026

Heavy-tailed random vectros: theory and applications

In this paper we introduce and study several multivariate, heavy-tailed distribution classes, and we explore their closure properties and their applications. We consider the class of multivariate, positively decreasing distributions, and its intersection with other multivariate distribution classes.

math.PR↗

arXiv2026

Uniform asymptotics for a multidimensional renewal risk model with random number of delayed claims and multivariate subexponentiality

In this paper we examine a multivariate risk model, with common renewal counting process, constant interest rate, and each claim vector is accompanied by a random number of delayed claim vectors. The interest is focused on the asymptotic behavior of the entrance probability of the discounted aggregate claims into some rare-sets, over a finite and an infinite time horizon. Our results study the the case where the main claims and the delayed claims have in some sense, asymptotic equivalent tails, but also the case where the delayed claims are negligible with comparisons with the main claims. More precisely, our estimations over finite time horizon are equipped with local uniformity, and are valid under the assumption of multivariate subexponential distributions for the claim distributions. On the case of infinite time horizon we need a mild restriction on the distribution class of multivariate subexponential distributions with positive lower Karamata index. The asymptotic relations reflect completely as all the sources of randomness, under the concrete rare-sets A, and the different dependence structures as well, without loosing elegance in spite of their generality. Further, we provide some more explicit formulas, together with relaxations of some assumptions, for the claim distributions from the multivariate regular variation. For the proof of the main results on infinite time case and for the construction of examples of multivariate distributions we need some closure properties of subexponential distributions with positive lower Karamata index. Especially, we present some necessary and sufficient conditions for the closure property with respect to convolution and some sufficient conditions for the closure property with respect to product convolution. Finally, we carry out some numerical studies to show the accuracy of our asymptotic estimations.

math.PR↗

arXiv2026

Asymptotics for a nonstandard risk model with multivariate subexponential claims and constant interest force

In this paper, the asymptotic behavior of the entrance probability of discounted aggregate claims of a certain family of rare sets is studied, considering the finite and infinite time horizons. This multivariate risk model, driven by a common counting process, has a constant interest rate and allows the interdependence of claim vectors. For the finite time horizon, the multivariate subexponential distribution of the common claim vector and the weak dependence structure of regression dependence are used. For the infinite time horizon, the claim vector is taken from a smaller distribution class, and the weak dependence structure is more general. Both results are derived under some additional assumptions on the moments of the counting process, which is fulfilled by all inhomogeneous renewal processes and many quasi-renewal processes, respectively. Moreover, the results are specialized to the multivariate regularly varying case, where more explicit results on the asymptotic behavior of the entrance probability of the discounted aggregate claims are derived. At the end of the paper, the results obtained are used to study the finite and infinite time horizon ruin problems of a risk model with eventual Brownian perturbations.

math.PR↗

arXiv2026

Infinite-time ruin probability of a multivariate renewal risk model with Brownian perturbations

We consider the multivariate risk model with common renewal process among the lines of business, and Brownian perturbations. Assuming that the integrated tail distribution of claims is multivariate subexponential, we establish an asymptotic relation for the infinite-time ruin probability. A more explicit expression is given in case of claim distribution from multivariate regular variation. The results indicate the insensitivity of the asymptotic behavior of the ruin probability with respect to Brownian perturbations. Furthermore, we show that a multivariate distribution with finite expectation, that belongs to the class of multivariate dominatedly varying and long-tailed distributions, possesses integrated tail distribution from the class of multivariate subexponential distributions, which makes easier the checking of conditions in the theorem.

math.PR↗

arXiv2025

Uniform asymptotics for a multidimensional renewal risk model with multivariate subexponential claims

In this paper, we study a multidimensional risk model with a common renewal process and in the presence of a constant interest force. The claim sizes are independent and identically distributed random vectors, with the distribution of dependent components belonging to the class of multivariate subexponential distributions. We establish locally uniform asymptotic estimations for the entrance probability of the discounted aggregate claims into some rare sets, and further derive asymptotic estimations uniformly over all the time horizons. Furthermore, we present some distribution examples that belong to these multivariate heavy-tailed distribution classes, which are not restricted only to the case of multivariate regular variation.

math.PR↗

arXiv2025

Multivariate subexponentiality and interplay of insurance and financial risks in a renwal risk model

In this paper we consider a multivariate risk model with common renewal process, while the logarithmic returns of the insurers investment portfolio, are described by a Levy process. In the two main results are established an asymptotic expression for the entrance probability of the discounted aggregate claims in some rare sets x A. This asymptotic expression highlights the multivariate linear single big jump principle in asymptotic behavior of these probabilities. In the first result, we are restricted in the case where the insurer makes risk free investments, and hence we consider a non-negative Levy process. We assume that the claim vectors follow a distribution from a class, introduced here, and represents a negligibly smaller subclass of multivariate subexponential distributions, since the additional requirement for positive lower Karamata index, looks as a mild condition. Further, we consider that the insurance and financial risks, satisfy a weak dependence structure. In the second result, we allow arbitrarily dependence between the two risks, and we assume that the distribution of their product, at each renewal epoch, belongs to the intersection of the class of multivariate subexponential positively decreasing distributions with multivariate dominatedly varying distributions. In this theorem we also permit risky investment, putting a condition to Laplace exponent of the Levy process. We also note that even in the special one-dimensional subcase the main results are new. Furthermore, we present two examples, where we demand only conditions for the marginal distributions of both risks and their dependence structure. Both examples, under the restriction on multivariate regularly varying distributions provide more explicit and elegant relations in relation with that established in the main results.

math.PR↗

arXiv2025

Background risk model in presence of heavy tails under dependence

In this paper, we examine two problems on applied probability, which are directly connected with the dependence in presence of heavy tails. The first problem, is related to max-sum equivalence of the randomly weighted sums in bi-variate set up. Introducing a new dependence, called Generalized Tail Asymptotic Independence, we establish the bi-variate max-sum equivalence, under a rather general dependence structure, when the primary random variables follow distributions from the intersection of the dominatedly varying and the long tailed distributions. On base of this max-sum equivalence, we provide a result about the asymptotic behavior of two kinds of ruin probabilities, over a finite time horizon, in a bi-variate renewal risk model, with constant interest rate. The second problem, is related to the asymptotic behavior of the Tail Distortion Risk Measure, in a static portfolio, called Background Risk Model. In opposite to other approaches on this topic, we use a general enough assumption, that is based on multivariate regular variation.

math.PR↗

arXiv2025

Joint tail of randomly weighted sums under generalized quasi asymptotic independence

In this paper we revisited the classical problem of max-sum equivalence of randomly weighted sums in two dimensions. In opposite to the most papers in literature, we consider that there exists some interdependence between the primary random variables, which is achieved by a combination of a new dependence structure with some two-dimensional heavy-tailed classes of distributions. Further, we introduce a new approach in two-dimensional regular varying distributions, that in contrast to well-established multivariate regularly varying distributions, is consistent with the multivariate non-linear single big jump principle. We study some closure properties of this, and of other two-dimensional classes. Our results contain the finite-time ruin probability in a two-dimensional discrete time risk model

math.PR↗

arXiv2025

Tail behavior of randomly weighted sums with interdependent summands

We reconsider a classical, well-studied problem from applied probability. This is the max-sum equivalence of randomly weighted sums, and the originality is because we manage to include interdependence among the primary random variables, as well as among primary random variables and random weights, as a generalization of previously published results. As a consequence we provide the finite-time ruin probability, in a discrete-time risk model. Furthermore, we established asymptotic bounds for the generalized moments of randomly weighted sums in the case of dominatedly varying primary random variables under the same dependence conditions. Finally, we give some results for randomly weighted and stopped sums under similar dependence conditions, with the restriction that the random weights are identically distributed, and the same holds for the primary random variables. Additionally, under these assumptions, we find asymptotic expressions for the random time ruin probability, in a discete-time risk model.

math.PR↗

arXiv2025

Closure properties and heavy tails: random vectors in the presence of dependence

This paper is organized in three parts closely related to closure properties of heavy-tailed distributions and heavy-tailed random vectors. In the first part we consider two random variables X and Y with distributions F and G respectively. We assume that these random variables satisfy one type of a weak dependence structure. Under some mild conditions, we examine whether their product convolution distribution H belongs in the same distribution class of the distribution F. Namely we establish the closure property with respect to the product convolution, under this specific weak dependence structure, in the classes ERV, C, D, M, OS, OL, PD and K. Further in the second part we introduce a new distribution class, which satisfies some closure properties such as product and mixture.Further, we provide some applications on randomly weighted sums and on discrete-time risk model with dependent insurance and financial risks. Although the multivariate regular variation is well-established distribution, it does not happen in other heavy tailed random vectors. Therefore in the third part we introduced the class of dominatedly varying vectors and positively decreasing random vectors and we study the closure property of the independent scalar product under. Furthermore we study the closure property of the first class under sum and mixture, and we study the distribution of stopped sums where the summands are random vectors which belongs to this class. Some of these results holds and for positively decreasing random vectors.

math.PR↗

arXiv2024

Uniform asymptotic estimates for ruin probabilities of a multidimensional risk model with cadlag returns and multivariate heavy tailed claims

We study a multidimensional renewal risk model, with common counting process and cadlag returns. Considering that the claim vectors have common distribution from some multivariate distribution class with heavy tail, are mutually weakly dependent, and each one has arbitrarily dependent components, we obtain uniformly asymptotic estimations for the probability of entrance of discounted aggregate claims into a some rare sets, over a finite time horizon. Direct consequence of the claim behavior is the estimation of the ruin probability of the model in some ruin sets. Further, restricting the distribution class of the claim vectors in the multivariate regular variation, the estimations still hold uniformly over the whole time horizon.

math.PR↗

arXiv2024

A new approach in two-dimensional heavy-tailed distributions

We consider a new approach in the definition of two-dimensional heavy-tailed distributions. Namely, we introduce the classes of two-dimensional long-tailed, of twodimensional dominatedly varying and of two-dimensional consistently varying distributions. Next, we define the closure property with respect to two-dimensional convolution and to joint max-sum equivalence in order to study if they are satisfied by these classes. Further we examine the joint behavior of two random sums, under generalized tail asymptotic independence. Afterward we study the closure property under scalar product and two dimensional product convolution and by these results we extended our main result in the case of jointly randomly weighted sums. Our results contained some applications where we establish the asymptotic expression of the ruin probability in a two-dimensional discrete-time risk model.

math.PR↗