arXiv subjects

Marek Teuerle

Publications and source records attributed to Marek Teuerle.

6 recordsLinked to original sources

arXiv2025

Modelling and valuation of catastrophe bonds across multiple regions

The insurance-linked securities (ILS) market, as a form of alternative risk transfer, has been at the forefront of innovative risk-transfer solutions. The catastrophe bond (CAT bond) market now represents almost half of the entire ILS market and is growing steadily. Since CAT bonds are often tied to risks in different regions, we follow this idea by constructing different pricing models that incorporate various scenarios of dependence between catastrophe losses in different areas. Namely, we consider independent, proportional, and arbitrary two-dimensional distribution cases. We also derive a normal approximation of the prices. Finally, to include the market price of risk, we apply Wang's transform. We illustrate the differences between the scenarios and the performance of the approximation on the Property Claim Services data.

q-fin.PR↗

arXiv2025

Design and valuation of multi-region CoCoCat bonds

This paper introduces a novel multidimensional insurance-linked instrument: a contingent convertible bond (CoCoCat bond) whose conversion trigger is activated by predefined natural catastrophes across multiple geographical regions. We develop such a model explicitly accounting for the complex dependencies between regional catastrophe losses. Specifically, we explore scenarios ranging from complete independence to proportional loss dependencies, both with fixed and random loss amounts. Utilizing change-of-measure techniques, we derive risk-neutral pricing formulas tailored to these diverse dependence structures. By fitting our model to real-world natural catastrophe data from Property Claim Services, we demonstrate the significant impact of inter-regional dependencies on the CoCoCat bond's pricing, highlighting the importance of multidimensional risk assessment for this innovative financial instrument.

q-fin.PR↗

arXiv2023

Ruin probability for the quota share model with~phase-type distributed claims

In this paper, we generalise the results presented in the literature for the ruin probability for the insurer--reinsurer model under a pro-rata reinsurance contract. We consider claim amounts that are described by a phase-type distribution that includes exponential, mixture of exponential, Erlang, and mixture of Erlang distributions. We derive the ruin probability formulas with the use of change-of-measure technique and present important special cases. We illustrate the usefulness of the introduced model by fitting it to the real-world loss data. With the use of statistical tests and graphical tools, we show that the mixture of Erlangs is well-fitted to the data and is superior to other considered distributions. This justifies the fact that the presented results can be useful in the context of risk assessment of co-operating insurance companies.

q-fin.MF↗

arXiv2019

Cross-codifference for bidimensional VAR(1) models with infinite variance

In this paper we consider the problem of a measure that allows us to describe the spatial and temporal dependence structure of multivariate time series with innovations having infinite variance. By using recent results obtained in the problem of temporal dependence structure of univariate stochastic processes, where the auto-codifference was used, we extend its idea and propose a cross-codifference measure for a general vector autoregressive model of order 1 (VAR(1)). Next, we derive an analytical results for VAR(1) model with Gaussian and sub-Gaussian innovations, that are characterized by finite and infinite variance, respectively. We emphasize that obtained expressions perfectly agree with the empirical counterparts. Moreover, we show that for the considered processes the cross-codifference simplifies to the well-established cross-covariance measure in case of Gaussian white noise. Last part of the work is devoted to the statistical estimation of VAR(1) parameters based on the empirical cross-codifference. Again, we demonstrate via Monte Carlo simulations that proposed methodology works correctly.

math.PR↗

arXiv2018

Scaling limits for Lévy walks with rests

In this paper we investigate the asymptotic properties of the wait-first and jump-first Lévy walk with rest, which is a generalization of standard jump-first and jump-first Lévy walk that assumes each waiting time in the model is a sum of two positive random variables. We investigate the asymptotic properties of the theses new-type waiting times. Next we use the previous results of this paper together with continuous mapping approach to establish the main result, which is a functional convergence in Skorokhod $\mathbb{J}_1$ topology for the Lévy walks with rests.

math.PR↗

arXiv2015

Fractional diffusion equation with distributed-order material derivative. Stochastic foundations

In this paper we present stochastic foundations of fractional dynamics driven by fractional material derivative of distributed order-type. Before stating our main result we present the stochastic scenario which underlies the dynamics given by fractional material derivative. Then we introduce a Levy walk process of distributed-order type to establish our main result, which is the scaling limit of the considered process. It appears that the probability density function of the scaling limit process fulfills, in a weak sense, the fractional diffusion equation with material derivative of distributed-order type.

math.PR↗