Tomita, Masashi; Takaoka, Koichiro; Ishizaka, Motokazu Some mathematical properties of the premium function and ruin probability of a generalized Cramér-Lundberg model driven by mixed Poisson processes. (English) Zbl 07922752 Japan J. Ind. Appl. Math. 41, No. 3, 1389-1412 (2024). MSC: 91B30 62P05 × Cite Format Result Cite Review PDF Full Text: DOI
Denisov, Denis; Gotthardt, Niklas; Korshunov, Dmitry; Wachtel, Vitali Probabilistic approach to risk processes with level-dependent premium rate. (English) Zbl 07915304 Insur. Math. Econ. 118, 142-156 (2024). MSC: 91G05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
van Kreveld, Lucas; Mandjes, Michel; Dorsman, Jan-Pieter Cramér-Lundberg asymptotics for spectrally positive Markov additive processes. (English) Zbl 07896850 Scand. Actuar. J. 2024, No. 6, 561-582 (2024). MSC: 91G05 60G51 60J20 × Cite Format Result Cite Review PDF Full Text: DOI OA License
Chadjiconstantinidis, Stathis; Xenos, Panos Improved bounds on tails of convolutions of compound distributions: application to ruin probabilities for the risk process perturbed by diffusion. (English) Zbl 07866537 J. Comput. Appl. Math. 445, Article ID 115835, 27 p. (2024). MSC: 62P05 91G05 60K25 × Cite Format Result Cite Review PDF Full Text: DOI
Hata, Hiroaki; Yasuda, Kazuhiro Expected power utility maximization with delay for insurers under the 4/2 stochastic volatility model. (English) Zbl 07831669 Math. Control Relat. Fields 14, No. 1, 16-50 (2024). Reviewer: Tamás Mátrai (Edinburgh) MSC: 91G05 60H30 93E20 × Cite Format Result Cite Review PDF Full Text: DOI
Cao, Jingyi; Young, Virginia R. Approximating the classical risk process by stable Lévy motion. (English) Zbl 1520.91098 Scand. Actuar. J. 2023, No. 7, 679-707 (2023). MSC: 91B05 60G51 91G05 × Cite Format Result Cite Review PDF Full Text: DOI
Behme, Anita; Strietzel, Philipp Lukas On moments of downward passage times for spectrally negative Lévy processes. (English) Zbl 1516.60028 J. Appl. Probab. 60, No. 2, 452-464 (2023). MSC: 60G51 60G40 91G05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Nguyen, Duy Phat; Borovkov, Konstantin Parisian ruin with random deficit-dependent delays for spectrally negative Lévy processes. (English) Zbl 1519.91219 Insur. Math. Econ. 110, 72-81 (2023). Reviewer: Tamás Mátrai (Edinburgh) MSC: 91G05 44A10 60G40 60G51 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Strietzel, Philipp Lukas; Behme, Anita Moments of the ruin time in a Lévy risk model. (English) Zbl 1508.91486 Methodol. Comput. Appl. Probab. 24, No. 4, 3075-3099 (2022). MSC: 91G05 60G51 60G40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv OA License
Azarbad, M.; Parham, G. A.; Alavi, S. M. R. Optimal multidimensional reinsurance policies under a common shock dependency structure. (English) Zbl 1505.91319 Eur. Actuar. J. 12, No. 2, 559-577 (2022). MSC: 91G05 93E20 49L20 × Cite Format Result Cite Review PDF Full Text: DOI
Shimizu, Yasutaka Asymptotic statistics in insurance risk theory. (English) Zbl 1512.62004 SpringerBriefs in Statistics. JSS Research Series in Statistics. Singapore: Springer (ISBN 978-981-16-9283-3/pbk; 978-981-16-9284-0/ebook). x, 110 p. (2021). Reviewer: Tamás Mátrai (Edinburgh) MSC: 62-02 62P05 60G51 62F12 62G20 91-02 91B05 91G05 91G70 × Cite Format Result Cite Review PDF Full Text: DOI
Delsing, Guusje; Mandjes, Michel A transient Cramér-Lundberg model with applications to credit risk. (English) Zbl 1477.60073 J. Appl. Probab. 58, No. 3, 721-745 (2021). MSC: 60G51 62P05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Cohen, Asaf; Young, Virginia R. Optimal dividend problem: asymptotic analysis. (English) Zbl 1464.91068 SIAM J. Financ. Math. 12, No. 1, 29-46 (2021). MSC: 91G05 93E20 60G99 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Masoumifard, Khaled; Zokaei, Mohammad Optimal dynamic reinsurance strategies in multidimensional portfolio. (English) Zbl 1460.91232 Stochastic Anal. Appl. 39, No. 1, 1-21 (2021). Reviewer: George Stoica (Saint John) MSC: 91G05 49L25 90C39 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Behme, Anita; Klüppelberg, Claudia; Reinert, Gesine Ruin probabilities for risk processes in a bipartite network. (English) Zbl 1468.60058 Stoch. Models 36, No. 4, 548-573 (2020). MSC: 60G51 05C80 91B05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Cohen, Asaf; Young, Virginia R. Rate of convergence of the probability of ruin in the Cramér-Lundberg model to its diffusion approximation. (English) Zbl 1447.91130 Insur. Math. Econ. 93, 333-340 (2020). MSC: 91G05 45J05 60J60 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Avram, F.; Banik, A. D.; Horvath, A. Ruin probabilities by Padé’s method: simple moments based mixed exponential approximations (Renyi, De Vylder, Cramér-Lundberg), and high precision approximations with both light and heavy tails. (English) Zbl 1422.91323 Eur. Actuar. J. 9, No. 1, 273-299 (2019). MSC: 91B30 60G51 62P05 × Cite Format Result Cite Review PDF Full Text: DOI
Jordanova, Pavlina K.; Stehlík, Milan On multivariate modifications of Cramer-Lundberg risk model with constant intensities. (English) Zbl 1411.62140 Stochastic Anal. Appl. 36, No. 5, 858-882 (2018). MSC: 62H12 62P05 60G10 45J05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Vidmar, Matija Ruin under stochastic dependence between premium and claim arrivals. (English) Zbl 1416.91223 Scand. Actuar. J. 2018, No. 6, 505-513 (2018). MSC: 91B30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Boldyreva, Valery O.; Shevchenko, G. M. On the continuous dependence of non-ruin probability on claim distribution function in the classical risk model. (English. Russian original) Zbl 1393.93113 Cybern. Syst. Anal. 54, No. 2, 242-248 (2018); translation from Kibern. Sist. Anal. 2018, No. 2, 78-84 (2018). MSC: 93E03 91B30 × Cite Format Result Cite Review PDF Full Text: DOI
Jordanova, P.; Nefedova, Y.; Stehlík, Milan Risk process approximation with mixing. (English) Zbl 1443.91005 Appl. Math. Modelling 41, 285-298 (2017). MSC: 91-10 91B05 × Cite Format Result Cite Review PDF Full Text: DOI
Belkina, Tatiana; Luo, Shangzhen Asymptotic investment behaviors under a jump-diffusion risk process. (English) Zbl 1414.91164 N. Am. Actuar. J. 21, No. 1, 36-62 (2017). MSC: 91B30 93E20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Schmidli, Hanspeter Risk theory. (English) Zbl 1422.91009 Springer Actuarial. Lecture Notes. Cham: Springer (ISBN 978-3-319-72004-3/pbk; 978-3-319-72005-0/ebook). xii, 242 p. (2017). Reviewer: Jonas Šiaulys (Vilnius) MSC: 91-01 91B30 91B16 60J75 60K10 × Cite Format Result Cite Review PDF Full Text: DOI
Clément, Dombry; Landy, Rabehasaina High order expansions for renewal functions and applications to ruin theory. (English) Zbl 1373.60150 Ann. Appl. Probab. 27, No. 4, 2342-2382 (2017). MSC: 60K05 60K10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Butler, Ronald W. Asymptotic expansions and hazard rates for compound and first-passage distributions. (English) Zbl 1407.60048 Bernoulli 23, No. 4B, 3508-3536 (2017). MSC: 60F99 60E07 62G32 62N01 × Cite Format Result Cite Review PDF Full Text: DOI Euclid
Hainaut, Donatien Contagion modeling between the financial and insurance markets with time changed processes. (English) Zbl 1394.91218 Insur. Math. Econ. 74, 63-77 (2017). MSC: 91B30 60J75 60G51 93E20 × Cite Format Result Cite Review PDF Full Text: DOI Link
Raju, I. Venkat Appal; Ramasubramanian, S. Risk diversifying treaty between two companies with only one in insurance business. (English) Zbl 1364.91070 Sankhyā, Ser. B 78, No. 2, 183-214 (2016). MSC: 91B30 60K10 62P05 × Cite Format Result Cite Review PDF Full Text: DOI
Albrecher, Hansjörg; Ivanovs, Jevgenijs; Zhou, Xiaowen Exit identities for Lévy processes observed at Poisson arrival times. (English) Zbl 1338.60125 Bernoulli 22, No. 3, 1364-1382 (2016). MSC: 60G51 60G55 91B30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Griffin, Philip S. Sample path behavior of a Lévy insurance risk process approaching ruin, under the Cramér-Lundberg and convolution equivalent conditions. (English) Zbl 1334.60076 Ann. Appl. Probab. 26, No. 1, 360-401 (2016). MSC: 60G51 60G17 60F17 91B30 62P05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Wüthrich, Mario V. From ruin theory to solvency in non-life insurance. (English) Zbl 1401.91202 Scand. Actuar. J. 2015, No. 6, 516-526 (2015). MSC: 91B30 × Cite Format Result Cite Review PDF Full Text: DOI
Ben-Salah, Zied; Guérin, Hélène; Morales, Manuel; Omidi Firouzi, Hassan On the depletion problem for an insurance risk process: new non-ruin quantities in collective risk theory. (English) Zbl 1396.91292 Eur. Actuar. J. 5, No. 2, 381-425 (2015). Reviewer: Tamás Mátrai (Budapest) MSC: 91B30 60J75 60G51 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Tran, Dong Xuan Padé approximants for finite time ruin probabilities. (English) Zbl 1301.91020 J. Comput. Appl. Math. 278, 130-137 (2015). MSC: 91B30 41A21 65C99 × Cite Format Result Cite Review PDF Full Text: DOI
Avram, F.; Pistorius, M. On matrix exponential approximations of ruin probabilities for the classic and Brownian perturbed Cramér-Lundberg processes. (English) Zbl 1306.91068 Insur. Math. Econ. 59, 57-64 (2014). MSC: 91B30 × Cite Format Result Cite Review PDF Full Text: DOI
Zhu, Jinxia Singular optimal dividend control for the regime-switching Cramér-Lundberg model with credit and debit interest. (English) Zbl 1291.91138 J. Comput. Appl. Math. 257, 212-239 (2014). MSC: 91B30 91G50 × Cite Format Result Cite Review PDF Full Text: DOI
Leng, Xuan; Hu, Taizhong The closure property of 2RV under random sum. (English) Zbl 1304.60060 Stat. Probab. Lett. 92, 158-167 (2014). Reviewer: Michael Falk (Würzburg) MSC: 60G70 62P05 × Cite Format Result Cite Review PDF Full Text: DOI
Pacheco González, Carlos G. Ruin probabilities and the ruin time distribution. (English) Zbl 1311.60099 Bol. Soc. Mat. Mex., III. Ser. 19, No. 1, 101-109 (2013). Reviewer: Hanspeter Schmidli (Köln) MSC: 60K05 91B30 45D05 65R20 × Cite Format Result Cite Review PDF
Dassios, Angelos; Zhao, Hongbiao A risk model with delayed claims. (English) Zbl 1278.91084 J. Appl. Probab. 50, No. 3, 686-702 (2013). Reviewer: Anatoliy Swishchuk (Calgary) MSC: 91B30 60G55 60F05 × Cite Format Result Cite Review PDF Full Text: DOI Euclid
Dassios, Angelos; Zhao, Hongbiao Ruin by dynamic contagion claims. (English) Zbl 1284.91224 Insur. Math. Econ. 51, No. 1, 93-106 (2012). MSC: 91B30 60J25 60J75 60J85 × Cite Format Result Cite Review PDF Full Text: DOI
Azcue, Pablo; Muler, Nora Optimal dividend policies for compound Poisson processes: the case of bounded dividend rates. (English) Zbl 1284.91201 Insur. Math. Econ. 51, No. 1, 26-42 (2012). MSC: 91B30 × Cite Format Result Cite Review PDF Full Text: DOI
Kelbert, Mark Ya.; Sazonov, Igor A.; Avram, Florin Uniform asymptotics of ruin probabilities for Lévy processes. (English) Zbl 1287.60060 Markov Process. Relat. Fields 18, No. 4, 681-692 (2012). MSC: 60G51 91B30 × Cite Format Result Cite Review PDF
Bondarev, B. V.; Boldyreva, V. O. On the non-ruin probability for the model of insurance company with the cost of advertising. I. (Russian. English summary) Zbl 1289.91070 Prykl. Stat., Aktuarna Finans. Mat. 2012, No. 2, 47-65 (2012). MSC: 91B30 62P05 × Cite Format Result Cite Review PDF
Korn, Ralf; Menkens, Olaf; Steffensen, Mogens Worst-case-optimal dynamic reinsurance for large claims. (English) Zbl 1269.91044 Eur. Actuar. J. 2, No. 1, 21-48 (2012). MSC: 91B30 × Cite Format Result Cite Review PDF Full Text: DOI Link
Golubin, A. Yu.; Gridin, V. N. Optimizing insurance and reinsurance in the dynamic Cramér-Lundberg model. (English. Russian original) Zbl 1258.93121 Autom. Remote Control 73, No. 9, 1529-1538 (2012); translation from Avtom. Telemekh. 2012, No. 9, 111-123 (2012). MSC: 93E20 91B30 49K45 × Cite Format Result Cite Review PDF Full Text: DOI
Bondarev, B. V.; Orfinyak, Ye. Yu. Application of statistical modelling methods for finding the non-ruin probability in the classical insurance model. II. (Russian. English summary) Zbl 1248.62199 Prykl. Stat., Aktuarna Finans. Mat. 2011, No. 1-2, 168-183 (2011). MSC: 62P05 91B30 65C05 × Cite Format Result Cite Review PDF
Ekheden, Erland; Silvestrov, Dmitrii Coupling and explicit rate of convergence in Cramér-Lundberg approximation for reinsurance risk processes. (English) Zbl 1315.91032 Commun. Stat., Theory Methods 40, No. 19-20, 3524-3539 (2011). MSC: 91B30 60K05 60K10 62P05 × Cite Format Result Cite Review PDF Full Text: DOI
Albrecher, Hansjörg; Bäuerle, Nicole; Thonhauser, Stefan Optimal dividend-payout in random discrete time. (English) Zbl 1233.91139 Stat. Risk. Model. 28, No. 3, 251-276 (2011). Reviewer: Hanspeter Schmidli (Köln) MSC: 91B30 93E20 60K10 60J05 × Cite Format Result Cite Review PDF Full Text: DOI Link
Ramasubramanian, S. Multidimensional insurance model with risk-reducing treaty. (English) Zbl 1237.91137 Stoch. Models 27, No. 3, 363-387 (2011). MSC: 91B30 60H30 60J35 × Cite Format Result Cite Review PDF Full Text: DOI
Silvestrov, Dmitrii S. Nonlinearly perturbed stochastic processes and systems. (English) Zbl 1404.60130 Rykov, Vladimir V. (ed.) et al., Mathematical and statistical models and methods in reliability. Applications to medicine, finance, and quality control. Invited papers based on the presentation at the 6th international conference (MMR 2009), Moscow, Russia, June 22–26, 2009. Boston, MA: Birkhäuser (ISBN 978-0-8176-4970-8/hbk; 978-0-8176-4971-5/ebook). Statistics for Industry and Technology, 19-37 (2010). MSC: 60K05 60K15 60K10 60K20 60-02 × Cite Format Result Cite Review PDF Full Text: DOI
Pial Das, Kumer Bounding the ruin probability under force of interest. (English) Zbl 1322.91051 J. Appl. Probab. Stat. 5, No. 1, 119-127 (2010). MSC: 91G10 60G44 62P05 × Cite Format Result Cite Review PDF Full Text: Link
Bondarev, B. V.; Orfinyak, Ye. Yu. Application of statistical modelling methods for finding the non-ruin probability in the classical insurance model. I. (Russian. English summary) Zbl 1248.62198 Prykl. Stat., Aktuarna Finans. Mat. 2010, No. 1-2, 161-173 (2010). MSC: 62P05 91B30 65C05 × Cite Format Result Cite Review PDF
Golubin, A. Yu.; Gridin, V. N. Optimal insurance strategies in a risk process with restrictions on policyholder risks. (English. Russian original) Zbl 1205.49049 Autom. Remote Control 71, No. 8, 1578-1589 (2010); translation from Avtom. Telemekh. 2010, No. 8, 79-91 (2010). MSC: 49N90 91B30 93E20 × Cite Format Result Cite Review PDF Full Text: DOI
Azcue, Pablo; Muler, Nora Optimal investment policy and dividend payment strategy in an insurance company. (English) Zbl 1196.91033 Ann. Appl. Probab. 20, No. 4, 1253-1302 (2010). Reviewer: Georgiy Shevchenko (Kiev) MSC: 91B30 91G50 91B70 49L25 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Minkova, L. D. Compound compound Poisson risk model. (English) Zbl 1224.91078 Serdica Math. J. 35, No. 3, 301-310 (2009). MSC: 91B30 60K10 62P05 × Cite Format Result Cite Review PDF
Azcue, Pablo; Muler, Nora Optimal investment strategy to minimize the ruin probability of an insurance company under borrowing constraints. (English) Zbl 1156.91391 Insur. Math. Econ. 44, No. 1, 26-34 (2009). MSC: 91B30 91B28 60G40 × Cite Format Result Cite Review PDF Full Text: DOI
Kartashov, M. V. Inhomogeneous perturbations of a renewal equation and the Cramér-Lundberg theorem for a risk process with variable premium rates. (Ukrainian, English) Zbl 1224.91065 Teor. Jmovirn. Mat. Stat. 78, 54-65 (2008); translation in Theory Probab. Math. Stat. 78, 61-73 (2009). Reviewer: Mikhail P. Moklyachuk (Kyïv) MSC: 91B30 60K05 62P05 60A05 60J45 × Cite Format Result Cite Review PDF Full Text: DOI
Avram, Florin; Palmowski, Zbigniew; Pistorius, Martijn R. Exit problem of a two-dimensional risk process from the quadrant: Exact and asymptotic results. (English) Zbl 1163.60010 Ann. Appl. Probab. 18, No. 6, 2421-2449 (2008). Reviewer: Alexandra Rodkina (Kingston/Jamaica) MSC: 60F10 60G50 60G55 62P05 91B30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Asmussen, Søren; Pihlsgård, Mats Loss rates for Lévy processes with two reflecting barriers. (English) Zbl 1341.60036 Math. Oper. Res. 32, No. 2, 308-321 (2007). MSC: 60G51 60K10 60K25 × Cite Format Result Cite Review PDF Full Text: DOI Link
Meng, Hui; Zhang, Chunsheng; Wu, Rong On a joint distribution for the classical risk process with a stochastic return on investments. (English) Zbl 1183.60034 Stoch. Models 23, No. 3, 513-522 (2007). MSC: 60K10 60K05 91B30 60J75 62P05 × Cite Format Result Cite Review PDF Full Text: DOI
Liu, Guoxin; Wang, Ying; Zhang, Bei Ruin probability in the continuous-time compound binomial model. (English) Zbl 1110.62146 Insur. Math. Econ. 36, No. 3, 303-316 (2005). MSC: 62P05 91B30 60G35 60G44 × Cite Format Result Cite Review PDF Full Text: DOI
Azcue, Pablo; Muler, Nora Optimal reinsurance and dividend distribution policies in the Cramér-Lundberg model. (English) Zbl 1136.91016 Math. Finance 15, No. 2, 261-308 (2005). Reviewer: Krzysztof Szajowski (Wrocław) MSC: 91B30 49L20 49L25 60G07 93E20 × Cite Format Result Cite Review PDF Full Text: DOI
Schäl, Manfred On discrete-time dynamic programming in insurance: exponential utility and minimizing the ruin probability. (English) Zbl 1141.91031 Scand. Actuar. J. 2004, No. 3, 189-210 (2004). Reviewer: N. M. Zinchenko (Kyïv) MSC: 91B30 90C39 90C15 62P05 × Cite Format Result Cite Review PDF Full Text: DOI
Schmidli, Hanspeter Cramér-Lundberg approximations for ruin probabilities of risk processes perturbed by diffusion. (English) Zbl 0837.62087 Insur. Math. Econ. 16, No. 2, 135-149 (1995). MSC: 62P05 60K05 60J70 91B30 × Cite Format Result Cite Review PDF Full Text: DOI
Asmussen, Søren; Rolski, Tomasz Risk theory in a periodic environment: The Cramér-Lundberg approximation and Lundberg’s inequality. (English) Zbl 0801.60091 Math. Oper. Res. 19, No. 2, 410-433 (1994). MSC: 60K30 60K25 60G55 × Cite Format Result Cite Review PDF Full Text: DOI
Embrechts, P.; Klüppelberg, C. Some aspects of insurance mathematics. (English. Russian original) Zbl 0803.62092 Theory Probab. Appl. 38, No. 2, 262-295 (1993); translation from Teor. Veroyatn. Primen. 38, No. 2, 374-416 (1993). MSC: 62P05 91B30 × Cite Format Result Cite Review PDF
Grandell, Jan Aspects of risk theory. (English) Zbl 0717.62100 Springer Series in Statistics. Probability and its Applications. New York etc.: Springer-Verlag. x, 175 p. DM 78.00 (1991). Reviewer: V.Schmidt MSC: 62P05 62-02 91B30 90-02 60G55 60K20 60K10 × Cite Format Result Cite Review PDF
Asmussen, Søren Risk theory in a Markovian environment. (English) Zbl 0684.62073 Scand. Actuarial J. 1989, No. 2, 69-100 (1989). MSC: 62P05 60J99 65C99 60J70 × Cite Format Result Cite Review PDF Full Text: DOI
Rosenlund, Stig Numerical calculation of the Cramér-Lundberg approximation. (English) Zbl 0679.62095 Scand. Actuarial J. 1989, No. 2, 119-122 (1989). MSC: 62P05 65C99 × Cite Format Result Cite Review PDF Full Text: DOI