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We consider the risk-neutral pricing of vanilla, digital and down-and-out call options when the underlying asset price evolves like the exponential of a Markov-modulated Brownian motion (MMBM) with two-sided phase-type jumps. The price of such options is intimately related to the first passage properties of the MMBM. To analyse these first passages, we randomize the time horizon using Erlang distributions with suitable parameters and apply matrix-analytic methods. This provides us with closed form approximations of the options prices, with a very high precision, as shown by several numerical illustrations. In particular, we consider an example in which the phase-type jump distribution is constructed in such a way that it mimics fat tails., SCOPUS: ar.j, info:eu-repo/semantics/published

This paper proposes efficient statistical tools to detect which risk factors influence insurance losses before fitting a regression model. The statistical procedures are nonparametric and designed according to the format of the variables commonly encountered in P&C ratemaking: continuous, integer-valued (or discrete) or categorical. The proposed approach improves the current practice favoring Chi-Square independence tests in contingency tables, avoiding the arbitrary preliminary banding of the variables under consideration. An example with motor insurance data illustrates the usefulness of the tools proposed in this paper. One of the conclusions of this numerical illustration is that zero-modified regression models are necessary to capture the impact of risk factors., info:eu-repo/semantics/published

In this article, we focus upon a family of matrix valued stochastic processes and study the problem of determining the smallest time such that their Laplace transforms become infinite. In particular, we concentrate upon the class of Wishart processes, which have proved to be very useful in different applications by their ability in describing non-trivial dependence. Thanks to this remarkable property we are able to explain the behavior of the explosion times for the Laplace transforms of the Wishart process and its time integral in terms of the relative importance of the involved factors and their correlations., SCOPUS: ar.j, info:eu-repo/semantics/published

CEPAR Working Paper 2019/6, info:eu-repo/semantics/nonPublished

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The Belgian Law of 20 July 2007 has drastically changed the Belgian private health insurance sector by making individual contracts lifelong with the technical basis (i.e. actuarial assumptions) fixed at policy issue. The goal of the Law is to ensure the accessibility to supplementary health coverage in order to protect policyholders from discrimination and exclusion, essentially when these operate on the basis of age. Due to the unpredictable nature of medical inflation risk and the difficulty to model future increases of health claims, the legislator introduced medical indices together with a specific updating mechanism, which aim at establishing standardized and fair premium adjustments across the sector. This paper considers two major issues of the current Belgian system. The first one is related to the transferability of the reserves, whereas the second one is related to age-discrimination. We discuss these issues and their interplay, and we address the conflict between the goal of the Law and the practical problems arising in the light of the actuarial techniques., SCOPUS: re.j, info:eu-repo/semantics/published

In order to determine an appropriate amount of premium, statistical goodness-of-fit criteria must be supplemented with actuarial ones when assessing performance of a given candidate pure premium. In this paper, concentration curves and Lorenz curves are shown to provide actuaries with effective tools to evaluate whether a premium is appropriate or to compare two competing alternatives. The idea is to compare the premium income for sub-portfolios gathering low risks (identified as low by means of the premiums under consideration) to the true one, or equivalently, to the actual losses. Numerical illustrations performed on hypothetical data and real ones demonstrate the usefulness of the proposed approach., SCOPUS: ar.j, info:eu-repo/semantics/published

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Dependence measures are often used in practice in order to assess the quality of a regression model. This is for instance the case with Kendall's tau and other association coefficients based on concordance probabilities. However, in case the response variable is discrete, correlation indices are often bounded and restricted to a sub-interval of [−1, 1]. Hence, in this context, small positive values of Kendall's tau may actually support goodness of prediction when getting close to its highest attainable value. In this paper, we derive the best-possible upper bounds for Kendall's tau when the response variable is discrete. Two cases are considered, depending on whether the score is continuous or discrete. Also, we illustrate the obtained upper bounds on a motor third-party liability insurance portfolio., SCOPUS: ar.j, info:eu-repo/semantics/published

Actuarial risk classification is usually performed at a guarantee and policyholder level: for each policyholder, the claim frequencies corresponding to each guarantee are modelled in isolation, without accounting for the correlation between the different guarantees and the different policyholders from the same household. However, sometimes, a common event will trigger both guarantees at the same time. Moreover, the claim frequencies for policyholders from the same household appear to be correlated. This paper aims to supplement the standard actuarial approach by combining two guarantees and the policyholders from the household, which allows to refine the prediction on the claim frequencies and account for the common shocks on multiple guarantees. Some possible cross-selling opportunities can also be identified., SCOPUS: ar.j, info:eu-repo/semantics/published

This paper addresses systematic longevity risk in long-term insurance business. We analyze the consequences of working under unknown survival probabilities on the efficiency of the Law of Large Numbers and point out the need for appropriate and feasible risk management techniques. We propose a setting for risk sharing schemes between the insurer and policyholders via a dynamic equivalence principle. We focus on a pure endowment contract and derive conditions for a viable risk sharing scheme which enhances the solvency situation of the insurer while being more favorably priced for the policyholders., SCOPUS: ar.j, info:eu-repo/semantics/published

Pay-how-you-drive (PHYD) or usage-based (UB) systems for automobile insurance provide actuaries with behavioural risk factors, such as the time of the day, average speeds and other driving habits. These data are collected while the contract is in force with the help of telematic devices installed in the vehicle. They thus fall in the category of a posteriori information that becomes available after contract initiation. For this reason, they must be included in the actuarial pricing by means of credibility updating mechanisms instead of being incorporated in the score as ordinary a priori observable features. This paper proposes the use of multivariate mixed models to describe the joint dynamics of telematics data and claim frequencies. Future premiums, incorporating past experience can then be determined using the predictive distribution of claim characteristics given past history. This approach allows the actuary to deal with the variety of situations encountered in insurance practice, ranging from new drivers without telematics record to contracts with different seniority and drivers using their vehicle to different extent, generating varied volumes of telematics data., SCOPUS: ar.j, info:eu-repo/semantics/published

Association measures based on concordance, such as Kendall's tau, Somers' delta or Goodmanand Kruskal's gamma are often used to measure explained variations in regressionmodels for binary outcomes. As responses only assume values in {0,1}, these associationmeasures are constrained, which makes their interpretation more difficult as a relativelysmall value may in fact strongly support the fitted model. In this paper, we derive the setof attainable values for concordance-based association measures in this setting so that thecloseness to the best-possible fit can be properly assessed., info:eu-repo/semantics/published

CEPAR Working Paper 2018/17, info:eu-repo/semantics/nonPublished

This paper considers the evaluation of spread and basket options when the underlying asset prices are driven by Markov-modulated Lévy processes with synchronous jumps. In particular, the asset prices may jump whenever there is a change of phase of the underlying Markov process. We further allow for dependence between the different price dynamics. In this general regime-switching framework, we provide lower and upper bounds to the exact option prices based upon ideas from the literature without regime switching. These bounds are obtained via univariate Fourier inversion under the assumption that the joint characteristic functions of the Markov-modulated Lévy processes are known. We study these obtained spread and basket option price approximations in different regime-switching models. Several numerical experiments are included and these show that, especially, the lower bounds have a very high precision., SCOPUS: cp.j, info:eu-repo/semantics/published

A way to model the clustering of jumps in asset prices consists in combining a diffusion process with a jump Hawkes process in the dynamics of the asset prices. This article proposes a new alternative model based on regime switching processes, referred to as a self-exciting switching jump diffusion (SESJD) model. In this model, jumps in the asset prices are synchronized with changes of states of a hidden Markov chain. The matrix of transition probabilities of this chain is designed in order to approximate the dynamics of a Hawkes process. This model presents several advantages compared to other jump clustering models. Firstly, the SESJD model is easy to fit to time series since estimation can be performed with an enhanced Hamilton filter. Secondly, the model explains various forms of option volatility smiles. Thirdly, several properties about the hitting times of the SESJD model can be inferred by using a fluid embedding technique, which leads to closed form expressions for some financial derivatives, like perpetual binary options., SCOPUS: ar.j, info:eu-repo/semantics/published

We propose a new approach for bivariate financial time series modelling which allows for mutual excitation between shocks. Jumps are triggered by changes of regime of a hidden Markov chain whose matrix of transition probabilities is constructed in order to approximate a bivariate Hawkes process. This model, called the Bivariate Mutually-Excited Switching Jump Diffusion (BMESJD) presents several interesting features. Firstly, compared to alternative approaches for modelling the contagion between jumps, the calibration is easier and performed with a modified Hamilton’s filter. Secondly, the BMESJD allows for simultaneous jumps when markets are highly stressed. Thirdly, a family of equivalent probability measures under which the BMESJD dynamics are preserved, is well identified. Finally, the BMESJD is a continuous time process that is well adapted for pricing options with two underlying assets., info:eu-repo/semantics/published

Actuarial risk classification studies are typically confined to univariate, policy-based analyses: individual claim frequencies are modelled for a single product, without accounting for the interactions between the different coverages bought by members of the same household. Now that large amounts of data are available and that the customer's value is at the heart of insurers' strategies, it becomes essential to develop multivariate risk models combining all the products subscribed by members of the household in order to capture the correlation effects. This paper aims to supplement the standard actuarial policy-based approach with a household-based approach. This makes the actuarial model more complex but also increases the volume of available information which eases and refines forecasting. Possible cross-selling opportunities can also be identified., SCOPUS: ar.j, info:eu-repo/semantics/published

This paper adopts the new loss reserving approach proposed by Denuit and Trufin (2016),inspired from the collective model of risk theory. But instead of considering the whole setof claims as a collective, two types of claims are distinguished, those claims with relativelyshort development patterns and claims requiring longer developments. In each case, thetotal payment per cell is modelled by means of a Compound Poisson distribution withappropriate assumptions about the severities. A case study based on a motor third partyliability insurance portfolio observed over 2004–2014 is used to illustrate the approachproposed in this paper. Comparisons with Chain-Ladder are performed and reveal significantdifferences in best estimates as well as in Value-at-Risk at high probability levels., SCOPUS: ar.j, info:eu-repo/semantics/published

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CEPAR Working Paper 2017/19, info:eu-repo/semantics/nonPublished

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This paper aims at showing how an ordering on claim amounts can influence finite-time ruin probabilities. Until now such a question was examined essentially for ultimate ruin probabilities. Over a finite horizon, a general approach does not seem possible but the study is conducted under different sets of conditions. This primarily covers the cases where the initial reserve is null or large, SCOPUS: ar.j, info:eu-repo/semantics/published

We propose an integrated model of the joint dynamics of FX rates and asset prices for the pricing of FX derivatives, including Quanto products; the model is based on a multivariate construction for Lévy processes which proves to be analytically tractable. The approach allows for simultaneous calibration to market volatility surfaces of currency triangles, and also gives access to market consistent information on dependence between the relevant variables. A successful joint calibration to real market data is presented for the particular case of the Variance Gamma process., SCOPUS: ar.j, info:eu-repo/semantics/published

This paper proposes a practical way for indexing level premiums inlifelong medical insurance contracts, in order to take into account observed medicalinflation. The indexing can be achieved by considering only premiums, withoutexplicit reference to reserves. This appears to be relevant in practice as reservingmechanisms may not be transparent to policyholders and as some mutual andshareholder insurers do not compute contract-specific reserves, managing the wholeportfolio in a collective way. Note that the similarity with the existing literature onlife insurance comes from the lifelong nature of the contracts considered in oursetting. However, in the case of health insurance covers the value of future benefitsis random. The present study originates from a proposal for indexing lifelongmedical insurance level premiums in Belgium. As an application, we study theimpact of various indexing mechanisms on a typical medical insurance portfolio onthe Belgian market., SCOPUS: ar.j, info:eu-repo/semantics/published

This paper studies the pricing of some multivariate European options, namely Exchange options and Quanto options, when the risky assets involved are modelled by Markov-Modulated Lévy Processes (MMLPs). Pricing formulae are based upon the characteristic exponents by using the well known FFT methodology. We study these pricing issues both under a risk neutral martingale measure and the historical measure. The dependence between the asset’s components is incorporated in the joint characteristic function of the MMLPs. As an example, we concentrate upon a regime-switching version of the model of Ballotta et al. (2015) in which the dependence structure is introduced in a flexible way. Several numerical examples are provided to illustrate our results., SCOPUS: ar.j, info:eu-repo/semantics/published

This paper proposes a new loss reserving approach, inspired from the collective model of risk theory. According to the collective paradigm, we do not relate payments to specific claims or policies but we work within a frequency-severity setting, with a number of payments in every cell of the run-off triangle, together with the corresponding paid amounts. Compared to the Tweedie reserving model, that can be seen as a compound sum with Poisson-distributed number of terms and Gamma-distributed summands, we allow here for more general severity distributions, typically mixture models combining a light-tailed component with a heavier-tailed one, including inflation effects. The severity model is fitted to individual observations and not to aggregated data displayed into run-off triangles with a single value in every cell. In that respect, the modeling approach appears to be a powerful alternative to both the crude traditional aggregated approach based on triangles and the extremely detailed individual reserving approach developing each and every claim separately. A case study based on a motor third party liability insurance portfolio observed over 2004-2014 is used to illustrate the relevance of the approach proposed in this paper., info:eu-repo/semantics/published

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