Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/195798 
Authors: 
Year of Publication: 
2018
Citation: 
[Journal:] Risks [ISSN:] 2227-9091 [Volume:] 6 [Issue:] 1 [Publisher:] MDPI [Place:] Basel [Year:] 2018 [Pages:] 1-14
Publisher: 
MDPI, Basel
Abstract: 
Optimal dividend payment under a ruin constraint is a two objective control problem which-in simple models-can be solved numerically by three essentially different methods. One is based on a modified Bellman equation and the policy improvement method (see Hipp (2003)). In this paper we use explicit formulas for running allowed ruin probabilities which avoid a complete search and speed up and simplify the computation. The second is also a policy improvement method, but without the use of a dynamic equation (see Hipp (2016)). It is based on closed formulas for first entry probabilities and discount factors for the time until first entry. Third a new, faster and more intuitive method which uses appropriately chosen barrier levels and a closed formula for the corresponding dividend value. Using the running allowed ruin probabilities, a simple test for admissibility-concerning the ruin constraint-is given. All these methods work for the discrete De Finetti model and are applied in a numerical example. The non stationary Lagrange multiplier method suggested in Hipp (2016), Section 2.2.2, also yields optimal dividend strategies which differ from those in all other methods, and Lagrange gaps are present here.
Subjects: 
stochastic control
optimal dividend payment
ruin probability constraint
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Document Type: 
Article
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