119 publications classées par:
type de publication
: Revue avec comité de lecture
Articles Albrecher H., Boxma O.J., Essifi R. & Kuijstermans R. (in press). A queueing model with randomized depletion of inventory. Probability in Engineering and Information Sciences. [pdf]
Albrecher H., Embrechts P., Filipovic D., Harrison G., Koch P., Loisel S. et al. (in press). Old-age provision: past, present, future. European Actuarial Journal. [doi]
Albrecher H. & Ivanovs J. (in press). Strikingly simple identities relating exit problems for Levy processes under continuous and Poisson observations. Stochastic Processes and Applications. [pdf]
Prettenthaler F., Albrecher H., Asadi P. & Koeberl J. (in press). On Flood Risk Pooling in Europe. Natural Hazards. [pdf]
Albrecher H., Ivanovs J. & Zhou X. (2016). Exit identities for Levy processes observed at Poisson arrival times. Bernoulli, 22(3), 1364-1382. [doi] [pdf] [web of science] [abstract]
For a spectrally one-sided Levy process, we extend various two-sided exit identities to the situation when the process is only observed at arrival epochs of an independent Poisson process. In addition, we consider exit problems of this type for processes reflected either from above or from below. The resulting Laplace transforms of the main quantities of interest are in terms of scale functions and turn out to be simple analogues of the classical formulas.
Albrecher H. & Lautscham V. (2015). Dividends and the Time of Ruin under Barrier Strategies with a Capital-Exchange Agreement. Anales del Instituto de Actuarios Espanoles, 21(3), 1-30. [pdf] [web of science] [abstract]
We consider a capital-exchange agreement, where two insurers recapitalize each other in certain situations with funds they would otherwise use for dividend payments. We derive equations characterizing the expected time of ruin and the expected value of the respective discounted dividends until ruin, if dividends are paid according to a barrier strategy. In a Monte Carlo simulation study we illustrate the potential advantages of this type of collaboration.
Kaas R., Gerber H., Goovaerts M., Shiu E. & Albrecher H. (2015). The impact factor of IME (Editorial). Insurance: Mathematics and Economics, 62, 1-4. [doi]
Albrecher H., Asadi P. & Ivanovs J. (2014). Exact boundaries in sequential testing for phase-type distributions. Journal of Applied Probability, 51A, 347-358. [doi] [pdf] [abstract]
Consider Wald's sequential probability ratio test for deciding whether a sequence of independent and identically distributed observations comes from a specified phase-type distribution or from an exponentially tilted alternative distribution. Exact decision boundaries for given type-I and type-II errors are derived by establishing a link with ruin theory. Information on the mean sample size of the test can be retrieved as well. The approach relies on the use of matrix-valued scale functions associated with a certain one-sided Markov additive process. By suitable transformations, the results also apply to other types of distributions, including some distributions with regularly varying tails.
Albrecher H., Avram F., Constantinescu C. & Ivanovs J. (2014). The tax identity for Markov additive risk processes. Methodology and Computing in Applied Probability, 16(1), 245-258. [doi] [pdf] [web of science] [abstract]
Taxed risk processes, i.e. processes which change their drift when reaching new maxima, represent a certain type of generalizations of Lévy and of Markov additive processes (MAP), since the times at which their Markovian mechanism changes are allowed to depend on the current position. In this paper we study generalizations of the tax identity of Albrecher and Hipp (2007) from the classical risk model to more general risk processes driven by spectrally-negative MAPs. We use the Sparre Andersen risk processes with phase-type interarrivals to illustrate the ideas in their simplest form.
Albrecher H., Boxma O.J. & Ivanovs J. (2014). On simple ruin expressions in dependent Sparre Andersen risk models. Journal of Applied Probability, 51(1), 293-296. [doi] [pdf] [web of science] [abstract]
In this note we provide a simple alternative probabilistic derivation of an explicit formula of Kwan and Yang (2007) for the probability of ruin in a risk model with a certain dependence between general claim interoccurrence times and subsequent claim sizes of conditionally exponential type. The approach puts the type of formula in a general context, illustrating the potential for similar simple ruin probability expressions in more general risk models with dependence.
Albrecher H. & Ivanovs J. (2014). Power identities for Lévy risk models under taxation and capital injections. Stochastic Systems, 4(1), 157-172. [doi] [pdf] [abstract]
In this paper we study a spectrally negative Lévy process which is refracted at its running maximum and at the same time reflected from below at a certain level. Such a process can for instance be used to model an insurance surplus process subject to tax payments according to a loss-carry-forward scheme together with the flow of minimal capital injections required to keep the surplus process non-negative. We characterize the first passage time over an arbitrary level and the cumulative amount of injected capital up to this time by their joint Laplace transform, and show that it satisfies a simple power relation to the case without refraction, generalizing results by Albrecher and Hipp (2007) and Albrecher, Renaud and Zhou (2008). It turns out that this identity can also be extended to a certain type of refraction from below. The net present value of tax collected before the cumulative injected capital exceeds a certain amount is determined, and a numerical illustration is provided.
Albrecher H., Robert C.Y. & Teugels J.L. (2014). Joint asymptotic distributions of smallest and largest insurance claims. Risks, 2(3), 289-314. [doi] [pdf] [abstract]
Assume that claims in a portfolio of insurance contracts are described by independent and identically distributed random variables with regularly varying tails and occur according to a near mixed Poisson process. We provide a collection of results pertaining to the joint asymptotic Laplace transforms of the normalised sums of the smallest and largest claims, when the length of the considered time interval tends to infinity. The results crucially depend on the value of the tail index of the claim distribution, as well as on the number of largest claims under consideration.
Albrecher H., Cheung E.C.K. & Thonhauser S. (2013). Randomized observation times for the compound Poisson risk model: The discounted penalty function. Scandinavian Actuarial Journal, 424-452. [doi] [pdf] [web of science] [abstract]
In the framework of collective risk theory, we consider a compound Poisson risk model for the surplus process where the process (and hence ruin) can only be observed at random observation times. For Erlang(n) distributed inter-observation times, explicit expressions for the discounted penalty function at ruin are derived. The resulting model contains both the usual continuous-time and the discrete-time risk model as limiting cases, and can be used as an effective approximation scheme for the latter. Numerical examples are given that illustrate the effect of random observation times on various ruin-related quantities.
Albrecher H., Constantinescu C., Palmowski Z., Regensburger M. & Rosenkranz M. (2013). Exact and asymptotic results for insurance risk models with surplus-dependent premiums. SIAM Journal of Applied Mathematics, 73(1), 47-66. [doi] [pdf] [web of science] [abstract]
In this paper we develop a symbolic technique to obtain asymptotic expressions for ruin probabilities and discounted penalty functions in renewal insurance risk models when the premium income depends on the present surplus of the insurance portfolio. The analysis is based on boundary problems for linear ordinary differential equations with variable coefficients. The algebraic structure of the Green's operators allows us to develop an intuitive way of tackling the asymptotic behavior of the solutions, leading to exponential-type expansions and Cramer-type asymptotics. Furthermore, we obtain closed-form solutions for more specific cases of premium functions in the compound Poisson risk model.
Albrecher H., Guillaume F. & Schoutens W. (2013). Implied liquidity: model sensitivity. Journal of Empirical Finance, 23, 48-67. [doi] [pdf] [web of science] [abstract]
The concept of implied liquidity originates from the conic finance theory and more precisely from the law of two prices where market participants buy from the market at the ask price and sell to the market at the lower bid price. The implied liquidity λ of any financial instrument is determined such that both model prices fit as well as possible the bid and ask market quotes. It reflects the liquidity of the financial instrument: the lower the λ, the higher the liquidity. The aim of this paper is to study the evolution of the implied liquidity pre- and post-crisis under a wide range of models and to study implied liquidity time series which could give an insight for future stochastic liquidity modeling. In particular, we perform a maximum likelihood estimation of the CIR, Vasicek and CEV mean-reverting processes applied to liquidity and volatility time series. The results show that implied liquidity is far less persistent than implied volatility as the liquidity process reverts much faster to its long-run mean. Moreover, a comparison of the parameter estimates between the pre- and post-credit crisis periods indicates that liquidity tends to decrease and increase for long and short term options, respectively, during troubled periods.
Albrecher H. & Ivanovs J. (2013). A risk model with an observer in a Markov environment. Risks, 1(3), 148-161. [doi] [pdf] [abstract]
We consider a spectrally-negative Markov additive process as a model of a risk process in a random environment. Following recent interest in alternative ruin concepts, we assume that ruin occurs when an independent Poissonian observer sees the process as negative, where the observation rate may depend on the state of the environment. Using an approximation argument and spectral theory, we establish an explicit formula for the resulting survival probabilities in this general setting. We also discuss an efficient evaluation of the involved quantities and provide a numerical illustration.
Albrecher H. & Lautscham V. (2013). From ruin to bankruptcy for compound Poisson surplus processes. ASTIN Bulletin, 43(2), 213-243. [doi] [pdf] [web of science] [abstract]
In classical risk theory, the infinite-time ruin probability of a surplus process Ct is calculated as the probability of the process becoming negative at some point in time. In this paper, we consider a relaxation of the ruin concept to the concept of bankruptcy, according to which one has a positive surplus-dependent probability to continue despite temporary negative surplus. We study the resulting bankruptcy probability for the compound Poisson risk model with exponential claim sizes for different bankruptcy rate functions, deriving analytical results, upper and lower bounds as well as an efficient simulation method. Numerical examples are given and the results are compared with the classical ruin probabilities. Finally, it is illustrated how the analysis can be extended to study the discounted penalty function under this relaxed ruin criterion.
Dacorogna M., Albrecher H., Moller M. & Sahiti S. (2013). Equalization Reserves for Natural Catastrophes and Shareholder Value: a Simulation Study. European Actuarial Journal, 3(1), 1-21. [doi] [pdf] [abstract]
This paper investigates the effects on the company value for shareholders of keeping equalization reserves for catastrophic risk in an insurance company. We perform an extensive simulation study to compare the performance of the company with and without equalization reserves for several standard profitability measures. Equalization reserves turn out to be beneficial for shareholders in terms of the resulting expected Sharpe ratio and also with respect to the value of the call option on assets at some reasonably large maturity time. Moreover, the expected total discounted tax payments are not smaller when using equalization reserves. The results are robust with respect to model parameters such as interest rate, time horizon, cost of raising capital and business cycle dynamics.
Dutang C., Albrecher H. & Loisel S. (2013). Competition among non-life insurers under solvency constraints: a game-theoretic approach. European Journal of Operational Research, 231(3), 702-711. [pdf]
Albrecher H., Asmussen S. & Kortschak D. (2012). Tail asymptotics for dependent subexponential differences. Siberian Mathematical Journal, 53(6), 965-983. [doi] [pdf] [web of science] [abstract]
We study the asymptotic behavior of ℙ(X − Y > u) as u → ∞, where X is subexponential, Y is positive, and the random variables X and Y may be dependent. We give criteria under which the subtraction of Y does not change the tail behavior of X. It is also studied under which conditions the comonotonic copula represents the worst-case scenario for the asymptotic behavior in the sense of minimizing the tail of X − Y. Some explicit construction of the worst-case copula is provided in other cases.
Albrecher H., Constantinescu C. & Thomann E. (2012). Asymptotic results for renewal risk models with risky investments. Stochastic Processes And Their Applications, 122(11), 3767-3789. [doi] [pdf] [web of science] [abstract]
We consider a renewal jump-diffusion process, more specifically a renewal insurance risk model with investments in a stock whose price is modeled by a geometric Brownian motion. Using Laplace transforms and regular variation theory, we introduce a transparent and unifying analytic method for investigating the asymptotic behavior of ruin probabilities and related quantities, in models with light- or heavy-tailed jumps, whenever the distribution of the time between jumps has rational Laplace transform.
Albrecher H., Kortschak D. & Zhou X. (2012). Pricing of Parisian options for a jump-diffusion model with two-sided jumps. Applied Mathematical Finance, 19(2), 97-129. [doi] [abstract]
Using the solution of one-sided exit problem, a procedure to price Parisian barrier options in a jump-diffusion model with two-sided exponential jumps is developed. By extending the method developed in Chesney, Jeanblanc-Picqué and Yor (1997; Brownian excursions and Parisian barrier options, Advances in Applied Probability, 29(1), pp. 165-184) for the diffusion case to the more general set-up, we arrive at a numerical pricing algorithm that significantly outperforms Monte Carlo simulation for the prices of such products.
Prettenthaler F., Albrecher H., Köberl J. & Kortschak D. (2012). Risk and insurability of storm damages to residential buildings in Austria. The Geneva Papers on Risk and Insurance - Issues and Practice, 37(2), 340-364. [doi] [web of science] [abstract]
This paper develops a stochastic model to assess storm risk in Austria, which relates wind speed and actual losses. By virtue of a building-stock-value-weighted wind index, we use suitably normalised historical loss data of residential buildings over 12 years and corresponding wind speed data to calibrate the model. Subsequently, additional wind speed data is used to generate further scenarios and to obtain loss curves for storm risk that give rise to storm insurance loss quantiles and corresponding solvency capital requirements both on the aggregate and on the regional level. We also investigate the diversification effect across regions and use tools from extreme value theory to assess the insurability of storm risk in Austria in general.
Albrecher H., Baeuerle N. & Thonhauser S. (2011). Optimal dividend payout in random discrete time. Statistics and Risk Modeling, 28(3), 251-276. [pdf]
Albrecher H., Borst S., Boxma O. & Resing J. (2011). Ruin excursions, the G/G/Infinity queue and tax payments in renewal risk models. Journal of Applied Probability, 48A, 3-14. [pdf]
Albrecher H., Cheung E.C.K. & Thonhauser S. (2011). Randomized observation times for the compound Poisson risk model: Dividends. ASTIN Bulletin, 41(2), 645-672. [pdf]
Albrecher H., Constantinescu C. & Loisel S. (2011). Explicit ruin formulas for models with dependence among risks. Insurance: Mathematics & Economics, 48(2), 265-270. [pdf]
Albrecher H. & Gerber H. (2011). A note on moments of dividends. Acta Mathematica Applicatae Sinica, 27(3), 353-354. [pdf]
Albrecher H., Gerber H. & Shiu E. (2011). The optimal dividend barrier in the Gamma-Omega model. European Actuarial Journal, 1(1), 43-55. [pdf]
Albrecher H. & Haas S. (2011). Ruin Theory with Excess of Loss Reinsurance and Reinstatements. Applied Mathematics and Computation, 217(20), 8031-8043. [pdf]
Thonhauser S. & Albrecher H. (2011). Optimal dividend strategies for a compound Poisson risk process under transaction costs and power utility. Stochastic Models, 27(1), 120-140. [pdf]
Trufin J., Albrecher H. & Denuit M. (2011). Properties of a risk measure derived from ruin theory. The Geneva Risk and Insurance Review, 36, 174-188. [pdf]
Trufin J., Albrecher H. & Denuit M. (2011). Ruin problems under IBNR Dynamics. Applied Stochastic Models in Business and Industry, 27(6), 619-632. [pdf]
Albrecher H., Avram F. & Kortschak D. (2010). On the efficient evaluation of ruin probabilities for completely monotone claim size distributions. Journal of Computational and Applied Mathematics, 233(10), 2724-2736. [pdf]
Albrecher H., Constantinescu C., Pirsic G., Regensburger G. & Rosenkranz M. (2010). An algebraic operator approach to the analysis of Gerber-Shiu functions. Insurance: Mathematics & Economics, 46(1), 42-51. [pdf]
Albrecher H., Gerber H. & Yang H. (2010). Reply to discussions on "A direct approach to the discounted penalty function". North American Actuarial Journal, 14(4), 445-447.
Albrecher H., Gerber H.U. & Yang H. (2010). A direct approach to the discounted penalty function. North American Actuarial Journal, 14(4), 420-434. [pdf]
Albrecher H., Hipp C. & Kortschak D. (2010). Higher-order expansions for compound distributions and ruin probabilities with subexponential claims. Scandinavian Actuarial Journal, 110(2), 105-135. [pdf]
Albrecher H., Ladoucette S. & Teugels J. (2010). Asymptotics of the Sample Coefficient of Variation and the Sample Dispersion. Journal of Statistical Planning and Inference, 140(2), 358-368. [pdf]
Kortschak D. & Albrecher H. (2010). An asymptotic expansion for the tail of compound sums of Burr distributed random variables. Statistics and Probability Letters, 80(7-8), 612-620. [pdf]
Albrecher H., Borst S., Boxma O. & Resing J. (2009). The tax identity in risk theory : a simple proof and an extension. Insurance: Mathematics & Economics, 44(2), 304-306.
Albrecher H. & Gerber H.U. (2009). On the non-optimality of proportional reinsurance according to the dividend criterion. Bulletin of the Swiss Association of Actuaries, 94-95. [pdf]
Albrecher H. & Kortschak D. (2009). On ruin probability and aggregate claim representations for Pareto claim size distributions. Insurance: Mathematics and Economics, 45(3), 362-373. [pdf]
Albrecher H., Scheicher K. & Teugels J. L. (2009). A combinatorial identity for a problem in asymptotic statistics. Applicable Analysis and Discrete Mathematics, 3(1), 64-68.
Albrecher H. & Thonhauser S. (2009). Optimality Results for Dividend Problems in Insurance. RACSAM Rev. R. Acad. Cien. Serie A. Mat., 103(2), 295-320. [pdf]
Kortschak D. & Albrecher H. (2009). Asymptotic results for the sum of dependent non-identically distributed random variables. Methodology and Computing in Applied Probability, 11(3), 279-306. [pdf]
Trufin J., Albrecher H. & Denuit M. (2009). Impact of underwriting cycles on the solvency of an insurance company. North American Actuarial Journal, 13(3), 385-403.
Albrecher H., Badescu A. & Landriault D. (2008). On the dual risk model with taxation. Insurance: Mathematics & Economics, 42(3), 1086-1094.
Albrecher H., Mayer P. & Schoutens W. (2008). General lower bounds for arithmetic Asian option prices. Applied Mathematical Finance, 15(2), 123-149. [pdf]
Albrecher H., Renaud J. & Zhou X. (2008). A Levy insurance risk process with tax. Journal of Applied Probability, 45(2), 363-375. [pdf]
Albrecher H. & Teugels J. L. (2008). On Excess-of-Loss Reinsurance. Theory of Probability and Mathematical Statistics, 79, 5-20.
Albrecher H. & Thonhauser S. (2008). Optimal dividend strategies for a risk process under force of interest. Insurance: Mathematics & Economics, 43, 134-149. [pdf]
Kindermann S., Mayer P., Albrecher H. & Engl H. (2008). Identification of the local speed function in a Levy model for option pricing. Journal of Integral Equations and Applications, 20(2), 161-200. [pdf]
Albrecher H. (2007). The next step : collateralized debt obligations for catastrophe risks. WILMOTT, 6, 16-18.
Albrecher H., Drmota M., Goldstern M., Grabner P. & Winkler R. (2007). Robert F.Tichy: 50 years - The unreasonable effectiveness of a number theorist. Uniform Distribution Theory, 2(1), 151-160.
Albrecher H. & Hartinger J. (2007). Reply to discussions on "A risk model with multi-layer dividend strategy". North American Actuarial Journal, 11(4), 141-142.
Albrecher H. & Hartinger J. (2007). A risk model with multi-layer dividend strategy. North American Actuarial Journal, 11(2), 43-64. [pdf]
Albrecher H., Hartinger J. & Thonhauser S. (2007). On exact solutions for dividend strategies of threshold and linear barrier type in a Sparre Andersen model. ASTIN Bulletin, 37(2), 203-233. [pdf]
Albrecher H. & Hipp C. (2007). Lundberg's risk process with tax. Blätter der DGVFM, 28(1), 13-28. [pdf]
Albrecher H., Mayer P., Schoutens W. & Tistaert J. (2007). The little Heston trap. WILMOTT, 83-92. [pdf]
Albrecher H. & Thonhauser S. (2007). Discussion of ''On the Merger of Two Companies'' by H. Gerber and E. Shiu. North American Actuarial Journal, 11(2), 157-159.
Thonhauser S. & Albrecher H. (2007). Dividend maximization under consideration of the time value of ruin. Insurance: Mathematics & Economics, 41(1), 163-184. [pdf]
Albrecher H. & Asmussen S. (2006). Ruin probabilities and aggregate claims distributions for shot noise Cox processes. Scandinavian Actuarial Journal, 86-110. [pdf]
Albrecher H., Asmussen S. & Kortschak D. (2006). Tail asymptotics for the sum of two heavy-tailed dependent risks. Extremes, 9(2), 107-130. [pdf]
Albrecher H., Burkard R. E. & Cela E. (2006). An asymptotical study of combinatorial optimization problems by means of statistical mechanics. Journal of Computational and Applied Mathematics, 186(1), 148-162. [pdf]
Albrecher H. & Hartinger J. (2006). On the non-optimality of horizontal barrier strategies in the Sparre Andersen model. Hermis J. Comp. Math. Appl., 7, 109-122. [pdf]
Albrecher H. & Teugels J. L. (2006). Exponential behavior in the presence of dependence in risk theory. Journal of Applied Probability, 43(1), 257-273. [pdf]
Albrecher H. & Teugels J. L. (2006). Asymptotic Analysis of a Measure of Variation. Theory of Probability and Mathematical Statistics, 74, 1-9. [pdf]
Albrecher H. & Thonhauser S. (2006). Discussion of ''Optimal Dividend Strategies in the Compound Poisson Model'' by H. Gerber and E. Shiu. North American Actuarial Journal, 10(3), 68-71.
Albrecher H. (2005). Discussion of ''The Time Value of Ruin in a Sparre Andersen Model'' by H. Gerber and E. Shiu. North American Actuarial Journal, 9(2), 71-74.
Albrecher H. (2005). Some Extensions of the Classical Ruin Model in Risk Theory. Grazer Math. Ber., 348, 1-14.
Albrecher H. (2005). A note on the asymptotic behaviour of bottleneck problems. Operations Research Letters, 33(2), 183-186. [pdf]
Albrecher H. & Boxma O. (2005). On the discounted penalty function in a Markov-dependent risk model. Insurance: Mathematics & Economics, 37(3), 650-672. [pdf]
Albrecher H., Claramunt M. & Marmol M. (2005). On the distribution of dividend payments in a Sparre Andersen model with generalized Erlang(n) interclaim times. Insurance: Mathematics & Economics, 37(2), 324-334. [pdf]
Albrecher H., Dhaene J., Goovaerts M. & Schoutens W. (2005). Static hedging of Asian options under Levy models. Journal of Derivatives, 12(3), 63-72. [pdf]
Albrecher H., Hartinger J. & Tichy R. (2005). On the distribution of dividend payments and the discounted penalty function in a risk model with linear dividend barrier. Scandinavian Actuarial Journal, 103-126. [pdf]
Albrecher H. (2004). Discussion of ''Optimal Dividends: Analysis with Brownian Motion'' by H. Gerber and E. Shiu. North American Actuarial Journal, 8(2), 111-113.
Albrecher H. & Boxma O. (2004). A ruin model with dependence between claim sizes and claim intervals. Insurance: Mathematics & Economics, 35(2), 245-254. [pdf]
Albrecher H., Hartinger J. & Tichy R. (2004). Quasi-Monte Carlo techniques for CAT bond pricing. Monte Carlo Methods & Appl., 10(3-4), 197-212. [pdf]
Albrecher H. & Predota M. (2004). On Asian option pricing for NIG Levy processes. Journal of Computational and Applied Mathematics, 172(1), 153-168.
Albrecher H., Hartinger J. & Tichy R. (2003). Multivariate approximation methods for the pricing of catastrophe-linked bonds. Internat. Ser. Numer. Math., 145, 21-39. [pdf]
Albrecher H., Kainhofer R. & Tichy R. (2003). Simulation methods in ruin models with non-linear dividend barriers. Math. Comput. Simulation, 62(3-6), 277-287.
Albrecher H. (2002). Metric distribution results for sequences (qna). Math. Slovaca, 52(2), 195-206. [pdf]
Albrecher H. & Kainhofer R. (2002). Risk theory with a non-linear dividend barrier. Computing, 68(4), 289-311. [pdf]
Albrecher H., Kainhofer R. & Tichy R. (2002). Efficient simulation techniques for a generalized ruin model. Grazer Math. Ber., 345, 79-110. [pdf]
Albrecher H. & Kantor J. (2002). Simulation of ruin probabilities for risk processes of Markovian type. Monte Carlo Methods & Appl., 8(2), 111-127. [pdf]
Albrecher H. & Predota M. (2002). Bounds and approximations for discrete Asian options in a variance-gamma model. Grazer Math. Ber., 345, 35-57. [pdf]
Albrecher H., Teugels J. & Tichy R. (2001). On a gamma series expansion for the time-dependent probability of collective ruin. Insurance Mathematics & Economics, 29(3), 345-355. [pdf]
Albrecher H., Matousek J. & Tichy R. (2000). Discrepancy of point sequences on fractal sets. Publ. Math. Debrecen, 56(3-4), 233-249. [pdf]
Albrecher H. & Tichy R. (2000). Zur Konvergenz eines Lösungsverfahrens für ein Risikomodell mit gammaverteilten Schäden. Bull. Swiss Actuarial Association, 115-127. [pdf]
Editorial Albrecher H., Constantinescu C. & Garrido J. (2010). Editorial on the Special Issue on Gerber-Shiu Functions. Insurance: Mathematics & Economics, 46(1), 1-2.
Livres Albrecher H., Binder A., Lautscham V. & Mayer P. (2013). Introduction to Quantitative Methods for Financial Markets. Birkhaeuser, Basel. [doi]
Prettenthaler F. & Albrecher H. (Eds.). (2012). Sturmschäden: Modellierung der versicherten Schäden in Österreich (8). Verlag der Österreichischen Akademie der Wissenschaften, Wien.
S. Asmussen & H. Albrecher (2010). Ruin probabilities (Second Edition, 14). World Scientific, New Jersey. [pdf]
Prettenthaler F. & Albrecher H. (Eds.). (2009). Hochwasser und dessen Versicherung in Österreich. Verlag der Österreichischen Akademie der Wissenschaften, Wien.
Albrecher H., Runggaldier W. & Schachermayer W. (Eds.). (2009). Advanced Financial Modelling. de Gruyter, Berlin. [pdf]
Albrecher H., Binder A. & Mayer P. (2009). Einführung in die Finanzmathematik. Birkhäuser, Basel.
Parties de livre
Chapitre Albrecher H. & Thonhauser S. (2012). On optimal dividend strategies in insurance with a random time horizon. Stochastic processes, finance and control. Festschrift for Robert Elliott. (pp. 157-180). World Scientific. [pdf] [abstract]
For the classical compound Poisson surplus process of an insurance portfolio we investigate the problem of how to optimally pay out dividends to shareholders if the criterion is to maximize the expected discounted dividend payments until the time of ruin or a random time horizon, whichever is smaller. We explicitly solve this problem for an exponential time horizon and exponential claim sizes. Furthermore, we study the case of an Erlang(2)¦time horizon by introducing an external state process and derive the solution under the assumption that the external state process is observable. The results are illustrated by numerical examples.
Albrecher H. (2010). Reinsurance. Encyclopedia of Quantitative Finance (pp. 1539-1543). Wiley, Chichester.
Albrecher H. & Mayer P. (2010). Semi-static hedging strategies for exotic options. In Kiesel R., Scherer M. & Zagst R. (Eds.), Alternative Investments and Strategies (pp. 345-373). World Scientific, Singapore.
Albrecher H. & Kortschak D. (2009). Quantitativer Nachvollzug des NATKAT-Modells fuer Oesterreich. Hochwasser und dessen Versicherung in Österreich (pp. 77-90). Verlag der Österreichischen Akademie der Wissenschaften, Wien.
Prettenthaler F., Albrecher H. & Kortschak D. (2009). Anreiztheoretische Analyse des NATKAT-Modells für Österreich. Hochwasser und dessen Versicherung in Österreich (pp. 105-114). Verlag der Österreichischen Akademie der Wissenschaften, Wien.
Albrecher H., Ladoucette S. A. & Schoutens W. (2007). A generic one-factor Levy model for pricing synthetic CDOs. In Fu M., Jarrow R., Yen J. & Elliott R. J. (Eds.), Advances in Mathematical Finance (pp. 259-278). Birkhäuser, Boston. [pdf]
Albrecher H. & Schoutens W. (2005). Static hedging of Asian options under stochastic volatility models using Fast Fourier transform. In Kyprianou A. et al. (Ed.), Exotic Options and Advanced Levy Models (pp. 129-148). Wiley, Chichester.
Albrecher H. (2004). Operational Time. Encyclopedia of Actuarial Science (Vol. 3, pp. 1207-1208). Wiley, Chichester.
Albrecher H. (2004). Markov Models in Actuarial Science. Encyclopedia of Actuarial Science (Vol. 2, pp. 1094-1096). Wiley, Chichester.
Actes de conférence (partie) Albrecher H. (2016). Asymmetric Information and Insurance. Cahiers de l'Institute Louis Bachélier, 20 (pp. 12-15).
Albrecher H. & Daily-Amir D. (2015). On competitive non-life insurance pricing under incomplete information. In Guillen M. (Ed.), Current Topics on Risk Analysis: ICRA 6 and Risk 2015 Conference (pp. 41-48).
Albrecher H. & Haas S. (2010). A numerical approach to ruin models with excess of loss reinsurance and reinstatements. Proceedings of COMPSTAT 2010, Springer (pp. 135-145).
Albrecher H. & Kortschak D. (2008). Asymptotic expansion of the ruin probability for Pareto claim size distributions. Proceedings of the Fourth Int. Workshop on Applied Probability, Compagniegne.
Albrecher H. & Macci C. (2008). Large deviation bounds for ruin probability estimators in some risk models with dependence. Proceedings of the Fourth Int. Workshop on Applied Probability, Compiegne.
Albrecher H., Rojas-Nandayapa L. & Asmussen S. (2005). On the tail behavior of heavy-tailed dependent sums. Proceedings of the Int. Workshop on Risk Theory, Florence.
Albrecher H. (2004). The Valuation of Asian Options for Market Models of Exponential Levy Type. Proceedings of the 2nd Actuarial and Financial Mathematics Day (pp. 11-20). Royal Flemish Academy of Belgium for Arts and Sciences, Brussels. [pdf]
Abstract Albrecher H. (in press). Simple Identities for Randomized Observations in Risk Theory [Abstract]. . The Mathematics and Statistics of Quantitative Risk Management, Oberwolfach Report.
Albrecher H. (2012). A relaxed ruin condition in insurance [Abstract]. . The Mathematics and Statistics of Quantitative Risk Management, Oberwolfach Report 7 (pp. 11).
Cahiers de recherche Albrecher H. (1998). Dependent Risks and Ruin Probabilities in Insurance. IIASA IR-98-072.
Thèses Asadi P., ALBRECHER H. (Dir.) (2016). Extremes on river networks and flood loss modeling. Université de Lausanne, Faculté des hautes études commerciales.
Lautscham V., Albrecher, H. (Dir.) (2013). Solvency modelling in insurance : quantitative aspects and simulation techniques. Université de Lausanne, Faculté des hautes études commerciales.
Haas S., Albrecher, H. (Dir.) (2012). Optimal reinsurance forms and solvency. Université de Lausanne, Faculté des hautes études commerciales.