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Company value with ruin constraint in a discrete model

Hipp, C.

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.

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Verlagsausgabe §
DOI: 10.5445/IR/1000088212
Veröffentlicht am 05.12.2018
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Finanzwirtschaft, Banken und Versicherungen (FBV)
Publikationstyp Zeitschriftenaufsatz
Publikationsjahr 2018
Sprache Englisch
Identifikator ISSN: 2227-9091
KITopen-ID: 1000088212
Erschienen in Risks
Verlag MDPI
Band 6
Heft 1
Seiten Art. Nr.: 1
Vorab online veröffentlicht am 07.01.2018
Schlagwörter stochastic control, optimal dividend payment, ruin probability constraint
Nachgewiesen in Scopus
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