Optimal dividends for a two-dimensional risk model with simultaneous ruin of both branches

We consider the optimal dividend problem in the so-called degenerate bivariate risk model under the assumption that the surplus of one branch may become negative. More specific, we solve the stochastic control problem of maximizing discounted dividends until simultaneous ruin of both branches of an...
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Autor*in:	Strietzel, Philipp Lukas [verfasserIn] Heinrich, Henriette Elisabeth [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2022

Rechteinformationen:	Open Access Namensnennung 4.0 International ; CC BY 4.0

Schlagwörter:	admissibility compound Poisson process degenerate risk model dividends dynamic programming principle Hamilton–Jacobi–Bellman equation optimal strategy simultaneous ruin stochastic control viscosity solution

Übergeordnetes Werk:	Enthalten in: Risks - Basel : MDPI, 2013, 10(2022), 6 vom: Juni, Artikel-ID 116, Seite 1-23
Übergeordnetes Werk:	volume:10 ; year:2022 ; number:6 ; month:06 ; elocationid:116 ; pages:1-23

Links:	Link aufrufen Link aufrufen

DOI / URN:	10.3390/risks10060116

Katalog-ID:	1816493171

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allfields	10.3390/risks10060116 doi (DE-627)1816493171 (DE-599)KXP1816493171 DE-627 ger DE-627 rda eng Strietzel, Philipp Lukas verfasserin aut Optimal dividends for a two-dimensional risk model with simultaneous ruin of both branches Philipp Lukas Strietzel and Henriette Elisabeth Heinrich 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier DE-206 Open Access Controlled Vocabulary for Access Rights http://purl.org/coar/access_right/c_abf2 We consider the optimal dividend problem in the so-called degenerate bivariate risk model under the assumption that the surplus of one branch may become negative. More specific, we solve the stochastic control problem of maximizing discounted dividends until simultaneous ruin of both branches of an insurance company by showing that the optimal value function satisfies a certain Hamilton–Jacobi–Bellman (HJB) equation. Further, we prove that the optimal value function is the smallest viscosity solution of said HJB equation, satisfying certain growth conditions. Under some additional assumptions, we show that the optimal strategy lies within a certain subclass of all admissible strategies and reduce the two-dimensional control problem to a one-dimensional one. The results are illustrated by a numerical example and Monte Carlo simulated value functions. DE-206 Namensnennung 4.0 International CC BY 4.0 cc https://creativecommons.org/licenses/by/4.0/ admissibility (dpeaa)DE-206 compound Poisson process (dpeaa)DE-206 degenerate risk model (dpeaa)DE-206 dividends (dpeaa)DE-206 dynamic programming principle (dpeaa)DE-206 Hamilton–Jacobi–Bellman equation (dpeaa)DE-206 optimal strategy (dpeaa)DE-206 simultaneous ruin (dpeaa)DE-206 stochastic control (dpeaa)DE-206 viscosity solution (dpeaa)DE-206 Heinrich, Henriette Elisabeth verfasserin aut Enthalten in Risks Basel : MDPI, 2013 10(2022), 6 vom: Juni, Artikel-ID 116, Seite 1-23 Online-Ressource (DE-627)737288485 (DE-600)2704357-5 (DE-576)379467852 2227-9091 nnns volume:10 year:2022 number:6 month:06 elocationid:116 pages:1-23 https://www.mdpi.com/2227-9091/10/6/116/pdf?version=1654158241 Verlag kostenfrei http://doi.org/10.3390/risks10060116 Resolving-System kostenfrei GBV_USEFLAG_U GBV_ILN_26 ISIL_DE-206 SYSFLAG_1 GBV_KXP GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2034 GBV_ILN_2055 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2129 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 GBV_ILN_2403 GBV_ILN_2403 ISIL_DE-LFER AR 10 2022 6 6 116 1-23 26 01 0206 4187285547 x1z 13-09-22 2403 01 DE-LFER 419509593X 00 --%%-- --%%-- n --%%-- l01 07-10-22 2403 01 DE-LFER http://doi.org/10.3390/risks10060116 2403 01 DE-LFER https://www.mdpi.com/2227-9091/10/6/116/pdf?version=1654158241
spelling	10.3390/risks10060116 doi (DE-627)1816493171 (DE-599)KXP1816493171 DE-627 ger DE-627 rda eng Strietzel, Philipp Lukas verfasserin aut Optimal dividends for a two-dimensional risk model with simultaneous ruin of both branches Philipp Lukas Strietzel and Henriette Elisabeth Heinrich 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier DE-206 Open Access Controlled Vocabulary for Access Rights http://purl.org/coar/access_right/c_abf2 We consider the optimal dividend problem in the so-called degenerate bivariate risk model under the assumption that the surplus of one branch may become negative. More specific, we solve the stochastic control problem of maximizing discounted dividends until simultaneous ruin of both branches of an insurance company by showing that the optimal value function satisfies a certain Hamilton–Jacobi–Bellman (HJB) equation. Further, we prove that the optimal value function is the smallest viscosity solution of said HJB equation, satisfying certain growth conditions. Under some additional assumptions, we show that the optimal strategy lies within a certain subclass of all admissible strategies and reduce the two-dimensional control problem to a one-dimensional one. The results are illustrated by a numerical example and Monte Carlo simulated value functions. DE-206 Namensnennung 4.0 International CC BY 4.0 cc https://creativecommons.org/licenses/by/4.0/ admissibility (dpeaa)DE-206 compound Poisson process (dpeaa)DE-206 degenerate risk model (dpeaa)DE-206 dividends (dpeaa)DE-206 dynamic programming principle (dpeaa)DE-206 Hamilton–Jacobi–Bellman equation (dpeaa)DE-206 optimal strategy (dpeaa)DE-206 simultaneous ruin (dpeaa)DE-206 stochastic control (dpeaa)DE-206 viscosity solution (dpeaa)DE-206 Heinrich, Henriette Elisabeth verfasserin aut Enthalten in Risks Basel : MDPI, 2013 10(2022), 6 vom: Juni, Artikel-ID 116, Seite 1-23 Online-Ressource (DE-627)737288485 (DE-600)2704357-5 (DE-576)379467852 2227-9091 nnns volume:10 year:2022 number:6 month:06 elocationid:116 pages:1-23 https://www.mdpi.com/2227-9091/10/6/116/pdf?version=1654158241 Verlag kostenfrei http://doi.org/10.3390/risks10060116 Resolving-System kostenfrei GBV_USEFLAG_U GBV_ILN_26 ISIL_DE-206 SYSFLAG_1 GBV_KXP GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2034 GBV_ILN_2055 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2129 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 GBV_ILN_2403 GBV_ILN_2403 ISIL_DE-LFER AR 10 2022 6 6 116 1-23 26 01 0206 4187285547 x1z 13-09-22 2403 01 DE-LFER 419509593X 00 --%%-- --%%-- n --%%-- l01 07-10-22 2403 01 DE-LFER http://doi.org/10.3390/risks10060116 2403 01 DE-LFER https://www.mdpi.com/2227-9091/10/6/116/pdf?version=1654158241
allfields_unstemmed	10.3390/risks10060116 doi (DE-627)1816493171 (DE-599)KXP1816493171 DE-627 ger DE-627 rda eng Strietzel, Philipp Lukas verfasserin aut Optimal dividends for a two-dimensional risk model with simultaneous ruin of both branches Philipp Lukas Strietzel and Henriette Elisabeth Heinrich 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier DE-206 Open Access Controlled Vocabulary for Access Rights http://purl.org/coar/access_right/c_abf2 We consider the optimal dividend problem in the so-called degenerate bivariate risk model under the assumption that the surplus of one branch may become negative. More specific, we solve the stochastic control problem of maximizing discounted dividends until simultaneous ruin of both branches of an insurance company by showing that the optimal value function satisfies a certain Hamilton–Jacobi–Bellman (HJB) equation. Further, we prove that the optimal value function is the smallest viscosity solution of said HJB equation, satisfying certain growth conditions. Under some additional assumptions, we show that the optimal strategy lies within a certain subclass of all admissible strategies and reduce the two-dimensional control problem to a one-dimensional one. The results are illustrated by a numerical example and Monte Carlo simulated value functions. DE-206 Namensnennung 4.0 International CC BY 4.0 cc https://creativecommons.org/licenses/by/4.0/ admissibility (dpeaa)DE-206 compound Poisson process (dpeaa)DE-206 degenerate risk model (dpeaa)DE-206 dividends (dpeaa)DE-206 dynamic programming principle (dpeaa)DE-206 Hamilton–Jacobi–Bellman equation (dpeaa)DE-206 optimal strategy (dpeaa)DE-206 simultaneous ruin (dpeaa)DE-206 stochastic control (dpeaa)DE-206 viscosity solution (dpeaa)DE-206 Heinrich, Henriette Elisabeth verfasserin aut Enthalten in Risks Basel : MDPI, 2013 10(2022), 6 vom: Juni, Artikel-ID 116, Seite 1-23 Online-Ressource (DE-627)737288485 (DE-600)2704357-5 (DE-576)379467852 2227-9091 nnns volume:10 year:2022 number:6 month:06 elocationid:116 pages:1-23 https://www.mdpi.com/2227-9091/10/6/116/pdf?version=1654158241 Verlag kostenfrei http://doi.org/10.3390/risks10060116 Resolving-System kostenfrei GBV_USEFLAG_U GBV_ILN_26 ISIL_DE-206 SYSFLAG_1 GBV_KXP GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2034 GBV_ILN_2055 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2129 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 GBV_ILN_2403 GBV_ILN_2403 ISIL_DE-LFER AR 10 2022 6 6 116 1-23 26 01 0206 4187285547 x1z 13-09-22 2403 01 DE-LFER 419509593X 00 --%%-- --%%-- n --%%-- l01 07-10-22 2403 01 DE-LFER http://doi.org/10.3390/risks10060116 2403 01 DE-LFER https://www.mdpi.com/2227-9091/10/6/116/pdf?version=1654158241
allfieldsGer	10.3390/risks10060116 doi (DE-627)1816493171 (DE-599)KXP1816493171 DE-627 ger DE-627 rda eng Strietzel, Philipp Lukas verfasserin aut Optimal dividends for a two-dimensional risk model with simultaneous ruin of both branches Philipp Lukas Strietzel and Henriette Elisabeth Heinrich 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier DE-206 Open Access Controlled Vocabulary for Access Rights http://purl.org/coar/access_right/c_abf2 We consider the optimal dividend problem in the so-called degenerate bivariate risk model under the assumption that the surplus of one branch may become negative. More specific, we solve the stochastic control problem of maximizing discounted dividends until simultaneous ruin of both branches of an insurance company by showing that the optimal value function satisfies a certain Hamilton–Jacobi–Bellman (HJB) equation. Further, we prove that the optimal value function is the smallest viscosity solution of said HJB equation, satisfying certain growth conditions. Under some additional assumptions, we show that the optimal strategy lies within a certain subclass of all admissible strategies and reduce the two-dimensional control problem to a one-dimensional one. The results are illustrated by a numerical example and Monte Carlo simulated value functions. DE-206 Namensnennung 4.0 International CC BY 4.0 cc https://creativecommons.org/licenses/by/4.0/ admissibility (dpeaa)DE-206 compound Poisson process (dpeaa)DE-206 degenerate risk model (dpeaa)DE-206 dividends (dpeaa)DE-206 dynamic programming principle (dpeaa)DE-206 Hamilton–Jacobi–Bellman equation (dpeaa)DE-206 optimal strategy (dpeaa)DE-206 simultaneous ruin (dpeaa)DE-206 stochastic control (dpeaa)DE-206 viscosity solution (dpeaa)DE-206 Heinrich, Henriette Elisabeth verfasserin aut Enthalten in Risks Basel : MDPI, 2013 10(2022), 6 vom: Juni, Artikel-ID 116, Seite 1-23 Online-Ressource (DE-627)737288485 (DE-600)2704357-5 (DE-576)379467852 2227-9091 nnns volume:10 year:2022 number:6 month:06 elocationid:116 pages:1-23 https://www.mdpi.com/2227-9091/10/6/116/pdf?version=1654158241 Verlag kostenfrei http://doi.org/10.3390/risks10060116 Resolving-System kostenfrei GBV_USEFLAG_U GBV_ILN_26 ISIL_DE-206 SYSFLAG_1 GBV_KXP GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2034 GBV_ILN_2055 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2129 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 GBV_ILN_2403 GBV_ILN_2403 ISIL_DE-LFER AR 10 2022 6 6 116 1-23 26 01 0206 4187285547 x1z 13-09-22 2403 01 DE-LFER 419509593X 00 --%%-- --%%-- n --%%-- l01 07-10-22 2403 01 DE-LFER http://doi.org/10.3390/risks10060116 2403 01 DE-LFER https://www.mdpi.com/2227-9091/10/6/116/pdf?version=1654158241
allfieldsSound	10.3390/risks10060116 doi (DE-627)1816493171 (DE-599)KXP1816493171 DE-627 ger DE-627 rda eng Strietzel, Philipp Lukas verfasserin aut Optimal dividends for a two-dimensional risk model with simultaneous ruin of both branches Philipp Lukas Strietzel and Henriette Elisabeth Heinrich 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier DE-206 Open Access Controlled Vocabulary for Access Rights http://purl.org/coar/access_right/c_abf2 We consider the optimal dividend problem in the so-called degenerate bivariate risk model under the assumption that the surplus of one branch may become negative. More specific, we solve the stochastic control problem of maximizing discounted dividends until simultaneous ruin of both branches of an insurance company by showing that the optimal value function satisfies a certain Hamilton–Jacobi–Bellman (HJB) equation. Further, we prove that the optimal value function is the smallest viscosity solution of said HJB equation, satisfying certain growth conditions. Under some additional assumptions, we show that the optimal strategy lies within a certain subclass of all admissible strategies and reduce the two-dimensional control problem to a one-dimensional one. The results are illustrated by a numerical example and Monte Carlo simulated value functions. DE-206 Namensnennung 4.0 International CC BY 4.0 cc https://creativecommons.org/licenses/by/4.0/ admissibility (dpeaa)DE-206 compound Poisson process (dpeaa)DE-206 degenerate risk model (dpeaa)DE-206 dividends (dpeaa)DE-206 dynamic programming principle (dpeaa)DE-206 Hamilton–Jacobi–Bellman equation (dpeaa)DE-206 optimal strategy (dpeaa)DE-206 simultaneous ruin (dpeaa)DE-206 stochastic control (dpeaa)DE-206 viscosity solution (dpeaa)DE-206 Heinrich, Henriette Elisabeth verfasserin aut Enthalten in Risks Basel : MDPI, 2013 10(2022), 6 vom: Juni, Artikel-ID 116, Seite 1-23 Online-Ressource (DE-627)737288485 (DE-600)2704357-5 (DE-576)379467852 2227-9091 nnns volume:10 year:2022 number:6 month:06 elocationid:116 pages:1-23 https://www.mdpi.com/2227-9091/10/6/116/pdf?version=1654158241 Verlag kostenfrei http://doi.org/10.3390/risks10060116 Resolving-System kostenfrei GBV_USEFLAG_U GBV_ILN_26 ISIL_DE-206 SYSFLAG_1 GBV_KXP GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2034 GBV_ILN_2055 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2129 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 GBV_ILN_2403 GBV_ILN_2403 ISIL_DE-LFER AR 10 2022 6 6 116 1-23 26 01 0206 4187285547 x1z 13-09-22 2403 01 DE-LFER 419509593X 00 --%%-- --%%-- n --%%-- l01 07-10-22 2403 01 DE-LFER http://doi.org/10.3390/risks10060116 2403 01 DE-LFER https://www.mdpi.com/2227-9091/10/6/116/pdf?version=1654158241
language	English
source	Enthalten in Risks 10(2022), 6 vom: Juni, Artikel-ID 116, Seite 1-23 volume:10 year:2022 number:6 month:06 elocationid:116 pages:1-23
sourceStr	Enthalten in Risks 10(2022), 6 vom: Juni, Artikel-ID 116, Seite 1-23 volume:10 year:2022 number:6 month:06 elocationid:116 pages:1-23
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institution	findex.gbv.de
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topic_facet	admissibility compound Poisson process degenerate risk model dividends dynamic programming principle Hamilton–Jacobi–Bellman equation optimal strategy simultaneous ruin stochastic control viscosity solution
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container_title	Risks
authorswithroles_txt_mv	Strietzel, Philipp Lukas @@aut@@ Heinrich, Henriette Elisabeth @@aut@@
publishDateDaySort_date	2022-06-01T00:00:00Z
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spellingShingle	Strietzel, Philipp Lukas misc admissibility misc compound Poisson process misc degenerate risk model misc dividends misc dynamic programming principle misc Hamilton–Jacobi–Bellman equation misc optimal strategy misc simultaneous ruin misc stochastic control misc viscosity solution Optimal dividends for a two-dimensional risk model with simultaneous ruin of both branches
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topic_title	Optimal dividends for a two-dimensional risk model with simultaneous ruin of both branches Philipp Lukas Strietzel and Henriette Elisabeth Heinrich admissibility (dpeaa)DE-206 compound Poisson process (dpeaa)DE-206 degenerate risk model (dpeaa)DE-206 dividends (dpeaa)DE-206 dynamic programming principle (dpeaa)DE-206 Hamilton–Jacobi–Bellman equation (dpeaa)DE-206 optimal strategy (dpeaa)DE-206 simultaneous ruin (dpeaa)DE-206 stochastic control (dpeaa)DE-206 viscosity solution (dpeaa)DE-206
topic	misc admissibility misc compound Poisson process misc degenerate risk model misc dividends misc dynamic programming principle misc Hamilton–Jacobi–Bellman equation misc optimal strategy misc simultaneous ruin misc stochastic control misc viscosity solution
topic_unstemmed	misc admissibility misc compound Poisson process misc degenerate risk model misc dividends misc dynamic programming principle misc Hamilton–Jacobi–Bellman equation misc optimal strategy misc simultaneous ruin misc stochastic control misc viscosity solution
topic_browse	misc admissibility misc compound Poisson process misc degenerate risk model misc dividends misc dynamic programming principle misc Hamilton–Jacobi–Bellman equation misc optimal strategy misc simultaneous ruin misc stochastic control misc viscosity solution
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title	Optimal dividends for a two-dimensional risk model with simultaneous ruin of both branches
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title_full	Optimal dividends for a two-dimensional risk model with simultaneous ruin of both branches Philipp Lukas Strietzel and Henriette Elisabeth Heinrich
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title_sort	optimal dividends for a two-dimensional risk model with simultaneous ruin of both branches
title_auth	Optimal dividends for a two-dimensional risk model with simultaneous ruin of both branches
abstract	We consider the optimal dividend problem in the so-called degenerate bivariate risk model under the assumption that the surplus of one branch may become negative. More specific, we solve the stochastic control problem of maximizing discounted dividends until simultaneous ruin of both branches of an insurance company by showing that the optimal value function satisfies a certain Hamilton–Jacobi–Bellman (HJB) equation. Further, we prove that the optimal value function is the smallest viscosity solution of said HJB equation, satisfying certain growth conditions. Under some additional assumptions, we show that the optimal strategy lies within a certain subclass of all admissible strategies and reduce the two-dimensional control problem to a one-dimensional one. The results are illustrated by a numerical example and Monte Carlo simulated value functions.
abstractGer	We consider the optimal dividend problem in the so-called degenerate bivariate risk model under the assumption that the surplus of one branch may become negative. More specific, we solve the stochastic control problem of maximizing discounted dividends until simultaneous ruin of both branches of an insurance company by showing that the optimal value function satisfies a certain Hamilton–Jacobi–Bellman (HJB) equation. Further, we prove that the optimal value function is the smallest viscosity solution of said HJB equation, satisfying certain growth conditions. Under some additional assumptions, we show that the optimal strategy lies within a certain subclass of all admissible strategies and reduce the two-dimensional control problem to a one-dimensional one. The results are illustrated by a numerical example and Monte Carlo simulated value functions.
abstract_unstemmed	We consider the optimal dividend problem in the so-called degenerate bivariate risk model under the assumption that the surplus of one branch may become negative. More specific, we solve the stochastic control problem of maximizing discounted dividends until simultaneous ruin of both branches of an insurance company by showing that the optimal value function satisfies a certain Hamilton–Jacobi–Bellman (HJB) equation. Further, we prove that the optimal value function is the smallest viscosity solution of said HJB equation, satisfying certain growth conditions. Under some additional assumptions, we show that the optimal strategy lies within a certain subclass of all admissible strategies and reduce the two-dimensional control problem to a one-dimensional one. The results are illustrated by a numerical example and Monte Carlo simulated value functions.
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title_short	Optimal dividends for a two-dimensional risk model with simultaneous ruin of both branches
url	https://www.mdpi.com/2227-9091/10/6/116/pdf?version=1654158241 http://doi.org/10.3390/risks10060116
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