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% Encoding: UTF-8
@book{cramer1930mathematical,
title={On the Mathematical Theory of Risk},
author={Cram{\'e}r, Harald},
year={1930},
publisher={Skandia Jubilee Volume, Stockholm}
}
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year = {1977},
volume = {40},
pages = {317--377},
}
@PhdThesis{nandayapa2008risk,
author = {Nandayapa, Leonardo Rojas},
title = {Risk probabilities: asymptotics and simulation},
school = {University of Aarhus, Department of Mathematical Sciences},
year = {2008},
}
@book{lundberg1903approximerad,
title={I. Approximerad {F}ramst{\"a}llning af {S}annolikhetsfunktionen, II. {\AA}terf{\"o}rs{\"a}kring af {K}ollektivrisker},
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year={1903},
publisher={Almqvist \& Wiksell, Uppsala}
}
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title = {Monte {C}arlo Estimation of the Density of the Sum of Dependent Random Variables},
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year = {2018},
note = {Under Revision},
}
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title={Recipe for disaster: The formula that killed {W}all {S}treet},
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@article{botev2017fast,
title={Fast and Accurate Computation of the Distribution of Sums of Dependent Log-Normals},
author={Botev, Zdravko I. and Salomone, Robert and MacKinlay, Daniel},
journal={arXiv Preprint 1705.03196},
year={2017}
}
@article{asmussen2017tail,
title={Tail asymptotics for light-tailed {W}eibull-like sums},
author={Asmussen, S{\o}ren and Hashorva, Enkelejd and Laub, Patrick J. and Taimre, Thomas},
journal={Probability and Mathematical Statistics},
volume={37},
number={2},
year={2017}
}
@book{cramer1926some,
title={On Some Classes of Series used in Mathematical Statistics},
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title={Panjer recursion versus {FFT} for compound distributions},
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@article{asmussen2018phase,
title={Phase-Type Models in Life Insurance: Fitting and Valuation of Equity-Linked Benefits},
author={S{\o}ren Asmussen and Jevgenijs Ivanovs and Patrick J. Laub and Hailiang Yang},
journal={Risks},
year={2018},
note={To be submitted}
}
@article{rojas2017asymptotic,
title={Asymptotic tail behaviour of phase-type scale mixture distributions},
author={Rojas-Nandayapa, Leonardo and Xie, Wangyue},
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year={2018},
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@inproceedings{yao2016estimating,
title={Estimating tail probabilities of random sums of infinite mixtures of phase-type distributions},
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year={2009},
school={Universit{\'e} de Montr{\'e}al}
}
@article{hassan2014use,
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@article{asmussen1996fitting,
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@article{bladt2005review,
title={A review on phase-type distributions and their use in risk theory},
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publisher={Cambridge University Press}
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@Manual{PDQutilsManual,
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{E}dgeworth, and {C}ornish {F}isher Approximations},
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year = {2017},
note = {R package version 0.1.6},
url = {https://github.com/shabbychef/PDQutils},
}
@article{cohen2011generalization,
title={On the generalization of the {E}dgeworth/{G}ram--{C}harlier series},
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pages={625--628},
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}
@article{berberan2007expressing,
title={Expressing a probability density function in terms of another {PDF}: A generalized {G}ram--{C}harlier expansion},
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@article{chateau2017gram,
title={{G}ram--{C}harlier Processes and Applications to Option Pricing},
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volume={volume 2017},
year={2017},
publisher={Hindawi}
}
@article{dufresne2000laguerre,
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@techreport{dufresne2016pricing,
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author={Dufresne, Daniel and Li, H.},
volume={2},
year={2016},
Institution={Actuarial Research Clearing House}
}
@article{popovic2012easy,
title={Easy {G}ram--{C}harlier valuations of options},
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year={2012},
publisher={Euromoney Institutional Investor PLC}
}
@article{hald2000early,
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}
@book{deuschel2001large,
title={Large Deviations},
author={Deuschel, Jean-Dominique and Stroock, Daniel W.},
volume={342},
year={2001},
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}
@book{foss2011introduction,
title={An Introduction to Heavy-Tailed and Subexponential Distributions},
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@article{mikosch2006Copula,
title = {Copulas: tales and facts},
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volume = {9},
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@article{cambou2017quasi,
title={Quasi-random numbers for copula models},
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pages={1307--1329},
year={2017},
publisher={Springer}
}
@article{cerou2007adaptive,
title={Adaptive multilevel splitting for rare event analysis},
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journal={Stochastic Analysis and Applications},
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pages={417--443},
year={2007},
publisher={Taylor \& Francis}
}
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title={Splitting for rare event simulation: analysis of simple cases},
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title={Rare Event Simulation using Monte Carlo Methods},
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title={Simulating heavy tailed processes using delayed hazard rate twisting},
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title={Loss Distribution Approach for Operational Risk},
author={Frachot, Antoine and Georges, Pierre and Roncalli, Thierry},
year={2001},
Institution={Groupe de Recherche Op{\'e}rationnelle, Cr{\'e}dit Lyonnais, France}
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@techreport{frachot2003loss,
title={Loss Distribution Approach in Practice},
author={Frachot, Antoine and Moudoulaud, Olivier and Roncalli, Thierry},
pages={527--555},
year={2003},
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}
@article{abate2006unified,
title={A unified framework for numerically inverting {L}aplace transforms},
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year={2006},
publisher={INFORMS}
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@article{abu1994outage,
title={Outage probabilities in the presence of correlated lognormal interferers},
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@book{aitchison1957lognormal,
title={The Lognormal Distribution with Special Reference to Its Uses in Economics},
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publisher={Cambridge University Press},
series={University of Cambridge Department of Applied Economics Monographs},
volume={5}
}
@article{beaulieu1995estimating,
title={Estimating the distribution of a sum of independent lognormal random variables},
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number={12},
pages={2869--2873},
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publisher={IEEE}
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title={On the {L}ambert {W} function},
author={Corless, Robert M. and Gonnet, Gaston H. and Hare, David E. G. and Jeffrey, David J. and Knuth, Donald E.},
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title={Regulatory Capital},
year={2010},
author={Duellmann, Klaus},
volume={IV},
pages={1525--1538},
booktitle={Encyclopedia of Quantitative Finance},
publisher={John Wiley \& Sons},
notes={DOI 10.1002/9780470061602.eqf15012}
}
@article{dufresne2004log,
title={The log-normal approximation in financial and other computations},
author={Dufresne, Daniel},
journal={Advances in Applied Probability},
volume={36},
number={3},
pages={747--773},
year={2004},
publisher={Applied Probability Trust}
}
@article{embrechts2014academic,
title={An academic response to {B}asel 3.5},
author={Embrechts, Paul and Puccetti, Giovanni and R{\"u}schendorf, Ludger and Wang, Ruodu and Beleraj, Antonela},
journal={Risks},
volume={2},
number={1},
pages={25--48},
year={2014},
publisher={Multidisciplinary Digital Publishing Institute}
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