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Dividend maximization in a hidden Markov switching model

Michaela Szölgyenyi

Abstract

In this paper we study the valuation problem of an insurance company by maximizing the expected discounted future dividend payments in a model with partial information that allows for a changing economic environment. The surplus process is modeled as a Brownian motion with drift. This drift depends on an underlying Markov chain the current state of which is assumed to be unobservable. The different states of the Markov chain thereby represent different phases of the economy. We apply results from filtering theory to overcome uncertainty and then we give an analytic characterization of the optimal value function. Finally, we present a numerical study covering various scenarios to get a clear picture of how dividends should be paid out.

Funding source: Vienna Science and Technology Fund (WWTF)

Award Identifier / Grant number: MA14-031

Funding statement: The author is supported by the Vienna Science and Technology Fund (WWTF) through project MA14-031. The main part of this paper was written while the author was member of the Department of Financial Mathematics and Applied Number Theory, Johannes Kepler University Linz, 4040 Linz, Austria. During this time, she was supported by the Austrian Science Fund (FWF) through project F5508-N26, which is part of the Special Research Program “Quasi-Monte Carlo Methods: Theory and Applications”.

The author thanks Gunther Leobacher (Johannes Kepler University Linz), Stefan Thonhauser (Graz University of Technology) and Ralf Wunderlich (BTU Cottbus-Senftenberg) for fruitful discussions and helpful advice that improved this paper. Furthermore, the author thanks two anonymous referees for their suggestions.

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Received: 2015-6-11
Revised: 2016-2-9
Accepted: 2016-2-11
Published Online: 2016-2-20
Published in Print: 2015-12-1

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