On the joint distribution of tax payments and capital injections for a Lévy risk model

• Autorzy: Albrecher H. , Ivanovs J.

Identyfikatory

DOI

10.19195/0208-4147.37.2.1

• Języki publikacji: EN

Abstrakty

EN

We study the joint distribution of tax payments according to a loss-carry-forward scheme and capital injections in a Lévy risk model, and provide a transparent expression for the corresponding transform in terms of the scale function. This allows us to identify the net present value of capital injections in such a model, complementing the one for tax found in our paper [3]. We also apply the result to the situation when injections may be stopped at a constant rate, and in this case an explicit formula for the net present value of taxes and injections is given.

Słowa kluczowe

EN

two-sided reflection; finite buffer; dividends; net present value; scale functions

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2017
• Tom: Vol. 37, Fasc. 2
• Strony: 219--227
• Opis fizyczny: Bibliogr. 15 poz., wykr.

Twórcy

autor

Albrecher H.

• University of Lausanne and Swiss Finance Institute, Quartier UNIL-Dorigny, Bâtiment Extranef, 1015 Lausanne, Switzerland

autor

Ivanovs J.

• Aarhus University, Ny Munkegade 118, DK-8000 Aarhus C, Denmark

Bibliografia

• [1] H. Albrecher, S. Borst, O. Boxma, and J. Resing, The tax identity in risk theory – a simple proof and an extension, Insurance Math. Econom. 44 (2) (2009), pp. 304-306.
• [2] H. Albrecher and C. Hipp, Lundberg’s risk process with tax, Bl. DGVFM 28 (1) (2007), pp. 13-28.
• [3] H. Albrecher and J. Ivanovs, Power identities for Lévy risk models under taxation and capital injections, Stoch. Syst. 4 (1) (2014), pp. 157-172.
• [4] H. Albrecher and J. Ivanovs, Linking dividends and capital injections – a probabilistic approach, Scand. Actuar. J. (to appear).
• [5] S. Asmussen, Applied Probability and Queues, second edition, Stoch. Model. Appl. Probab., Vol. 51, Springer, New York 2003.
• [6] F. Avram, Z. Palmowski, and M. Pistorius, On the optimal dividend problem for a spectrally negative Lévy process, Ann. Appl. Probab. 17 (1) (2007), pp. 156-180.
• [7] K. Dębicki and M. Mandjes, Queues and Lévy Fluctuation Theory, Universitext, Springer, Cham 2015.
• [8] D. Dickson and H. R. Waters, Some optimal dividends problems, Astin Bull. 34 (1) (2004), pp. 49-74.
• [9] H. U. Gerber and E. S. Shiu, Geometric Brownian motion models for assets and liabilities: From pension funding to optimal dividends, N. Am. Actuar. J. 7 (3) (2003), pp. 37-51.
• [10] J. Hugonnier and E. Morellec, Bank capital, liquid reserves, and insolvency risk, J. Financ. Econ. 125 (2) (2017), pp. 266-285.
• [11] J. Ivanovs, One-Sided Markov Additive Processes and Related Exit Problems, PhD dissertation, University of Amsterdam, Uitgeverij BOXPress, Oisterwijk 2011.
• [12] J. Ivanovs, Potential measures of one-sided Markov additive processes with reflecting and terminating barriers, J. Appl. Probab. 51 (4) (2014), pp. 1154-1170.
• [13] N. Kulenko and H. Schmidli, Optimal dividend strategies in a Cramér-Lundberg model with capital injections, Insurance Math. Econom. 43 (2) (2008), pp. 270-278.
• [14] A. Kuznetsov, A. E. Kyprianou, and V. Rivero, The theory of scale functions for spectrally negative Lévy processes, in: Lévy Matters II, Springer, 2013, pp. 97-186.
• [15] A. E. Kyprianou, Introductory Lectures on Fluctuations of Lévy Processes with Applications, Universitext, Springer, Berlin 2006.

Uwagi

Dedicated to Tomasz Rolski on the occasion of his 70th birthday.

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).