On a dividend problem with random funding
Tóm tắt
We consider a modification of the dividend maximization problem from ruin theory. Based on a classical risk process we maximize the difference of expected cumulated discounted dividends and total expected discounted additional funding (subject to some proportional transaction costs). For modelling dividends we use the common approach whereas for the funding opportunity we use the jump times of another independent Poisson process at which we choose an appropriate funding height. In case of exponentially distributed claims we are able to determine an explicit solution to the problem and derive an optimal strategy whose nature heavily depends on the size of the transaction costs. Furthermore, the optimal strategy identifies unfavourable surplus positions prior to ruin at which refunding is highly recommended.
Tài liệu tham khảo
Albrecher H, Cheung EC, Thonhauser S (2011) Randomized observation periods for the compound poisson risk model: dividends. ASTIN Bull 41(2):645–672
Azcue P, Muler N (2005) Optimal reinsurance and dividend distribution policies in the Cramér–Lundberg model. Math Financ 15(2):261–308
Azcue P, Muler N (2014) Stochastic optimization in insurance. Springer briefs in quantitative finance. Springer, New York
Azcue P, Muler N (2010) Optimal investment policy and dividend payment strategy in an insurance company. Ann Appl Probab 20(4):1253–1302
Binmore K, Rubinstein A, Wolinsky A (1986) The Nash bargaining solution in economic modelling. RAND J Econ 17(2):176–188
Gerber HU (1969) Entscheidungskriterien für den zusammengesetzten Poisson–Prozess. Schweiz Aktuarver Mitt 69(2):186–226
Hugonnier J, Malamud S, Morellec E (2015) Capital supply uncertainty, cash holdings, and investment. Rev Financ Stud 28(2):391–445
Hugonnier J, Malamud S, Morellec E (2015) Supplementary Appendix to: Capital supply uncertainty, cash holdings, and investment. https://www.epfl.ch/schools/cdm/wp-content/uploads/2018/08/HMM-App.pdf
Kulenko N, Schmidli H (2008) Optimal dividend strategies in a Cramér–Lundberg model with capital injections. Insur. Math. Econom. 43(2):270–278
Rolski T, Schmidli H, Schmidt V, Teugels JL (1999) Stochastic processes for insurance and finance. Wiley, New York
Schmidli H (2008) Stochastic control in insurance. Probability and its applications. Springer, Berlin
Shreve SE, Lehoczky JP, Gaver DP (1984) Optimal consumption for general diffusions with absorbing and reflecting barriers. SIAM J. Control Optim. 22(1):55–75
Zhang Z, Cheung EC, Yang H (2018) On the compound Poisson risk model with periodic capital injections. ASTIN Bull 48(1):435–477