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Erschienen in: Decisions in Economics and Finance 1/2020

13.08.2019

Optimal reinsurance and investment in a diffusion model

verfasst von: Matteo Brachetta, Hanspeter Schmidli

Erschienen in: Decisions in Economics and Finance | Ausgabe 1/2020

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Abstract

We consider a diffusion approximation to an insurance risk model where an external driver models a stochastic environment. The insurer can buy reinsurance. Moreover, it is possible to invest in a financial market that depends on the insurance market. The financial market is also driven by the environmental process. Our goal is to maximise terminal expected utility. In particular, we consider the case of SAHARA utility functions. In the case of proportional and excess-of-loss reinsurance, we obtain explicit results.
Literatur
Zurück zum Zitat Brachetta, M., Ceci, C.: Optimal excess-of-loss reinsurance for stochastic factor risk models. Risks 7(2), 48 (2019)CrossRef Brachetta, M., Ceci, C.: Optimal excess-of-loss reinsurance for stochastic factor risk models. Risks 7(2), 48 (2019)CrossRef
Zurück zum Zitat Brachetta, M., Ceci, C.: Optimal proportional reinsurance and investment for stochastic factor models. Insur. Math. Econ. 87, 15–33 (2019)CrossRef Brachetta, M., Ceci, C.: Optimal proportional reinsurance and investment for stochastic factor models. Insur. Math. Econ. 87, 15–33 (2019)CrossRef
Zurück zum Zitat Bühlmann, H.: Mathematical Methods in Risk Theory. Springer-Verlag, Berlin (1970) Bühlmann, H.: Mathematical Methods in Risk Theory. Springer-Verlag, Berlin (1970)
Zurück zum Zitat Chen, A., Pelsser, A., Vellekoop, M.: Modeling non-monotone risk aversion using sahara utility functions. J. Econ. Theory 146(5), 2075–2092 (2011)CrossRef Chen, A., Pelsser, A., Vellekoop, M.: Modeling non-monotone risk aversion using sahara utility functions. J. Econ. Theory 146(5), 2075–2092 (2011)CrossRef
Zurück zum Zitat de Finetti, B.: Il problema dei “pieni”. G. Ist. Ital. Attuari 11, 1–88 (1940) de Finetti, B.: Il problema dei “pieni”. G. Ist. Ital. Attuari 11, 1–88 (1940)
Zurück zum Zitat Eisenberg, J., Schmidli, H.: Optimal control of capital injections by reinsurance in a diffusion approximation. Blätter DGVFM 30, 1–13 (2009)CrossRef Eisenberg, J., Schmidli, H.: Optimal control of capital injections by reinsurance in a diffusion approximation. Blätter DGVFM 30, 1–13 (2009)CrossRef
Zurück zum Zitat Gerber, H.U.: An Introduction to Mathematical Risk Theory. Huebner Foundation Monographs (1979) Gerber, H.U.: An Introduction to Mathematical Risk Theory. Huebner Foundation Monographs (1979)
Zurück zum Zitat Guerra, M., Centeno, M.: Optimal reinsurance policy: the adjustment coefficient and the expected utility criteria. Insur. Math. Econ. 42(2), 529–539 (2008)CrossRef Guerra, M., Centeno, M.: Optimal reinsurance policy: the adjustment coefficient and the expected utility criteria. Insur. Math. Econ. 42(2), 529–539 (2008)CrossRef
Zurück zum Zitat Irgens, C., Paulsen, J.: Optimal control of risk exposure, reinsurance and investments for insurance portfolios. Insur. Math. Econ. 35, 21–51 (2004)CrossRef Irgens, C., Paulsen, J.: Optimal control of risk exposure, reinsurance and investments for insurance portfolios. Insur. Math. Econ. 35, 21–51 (2004)CrossRef
Zurück zum Zitat Liang, Z., Bayraktar, E.: Optimal reinsurance and investment with unobservable claim size and intensity. Insur. Math. Econ. 55, 156–166 (2014)CrossRef Liang, Z., Bayraktar, E.: Optimal reinsurance and investment with unobservable claim size and intensity. Insur. Math. Econ. 55, 156–166 (2014)CrossRef
Zurück zum Zitat Mania, M., Santacroce, M.: Exponential utility maximization under partial information. Fin. Stoch. 14(3), 419–448 (2010)CrossRef Mania, M., Santacroce, M.: Exponential utility maximization under partial information. Fin. Stoch. 14(3), 419–448 (2010)CrossRef
Zurück zum Zitat Promislow, S.D., Young, V.R.: Minimizing the probability of ruin when claims follow Brownian motion with drift. North Am. Actuar. J. 9(3), 109 (2005) Promislow, S.D., Young, V.R.: Minimizing the probability of ruin when claims follow Brownian motion with drift. North Am. Actuar. J. 9(3), 109 (2005)
Zurück zum Zitat Schmidli, H.: Optimal proportional reinsurance policies in a dynamic setting. Scand. Actuar. J. 2001(1), 55–68 (2001)CrossRef Schmidli, H.: Optimal proportional reinsurance policies in a dynamic setting. Scand. Actuar. J. 2001(1), 55–68 (2001)CrossRef
Zurück zum Zitat Schmidli, H.: On minimizing the ruin probability by investment and reinsurance. Ann. Appl. Probab. 12(3), 890–907 (2002)CrossRef Schmidli, H.: On minimizing the ruin probability by investment and reinsurance. Ann. Appl. Probab. 12(3), 890–907 (2002)CrossRef
Zurück zum Zitat Schmidli, H.: Stochastic Control in Insurance. Springer-Verlag, Berlin (2008) Schmidli, H.: Stochastic Control in Insurance. Springer-Verlag, Berlin (2008)
Zurück zum Zitat Schmidli, H.: Risk Theory. Springer International Publishing, Berlin (2018) Schmidli, H.: Risk Theory. Springer International Publishing, Berlin (2018)
Zurück zum Zitat Wagner, D.: Survey of measurable selection theorems. SIAM J. Control Optim. 15, 859–903 (1977)CrossRef Wagner, D.: Survey of measurable selection theorems. SIAM J. Control Optim. 15, 859–903 (1977)CrossRef
Metadaten
Titel
Optimal reinsurance and investment in a diffusion model
verfasst von
Matteo Brachetta
Hanspeter Schmidli
Publikationsdatum
13.08.2019
Verlag
Springer International Publishing
Erschienen in
Decisions in Economics and Finance / Ausgabe 1/2020
Print ISSN: 1593-8883
Elektronische ISSN: 1129-6569
DOI
https://doi.org/10.1007/s10203-019-00265-8

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