Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# Company Value with Ruin Constraint in a Discrete Model

Version 1 : Received: 7 December 2017 / Approved: 8 December 2017 / Online: 8 December 2017 (06:55:06 CET)

How to cite: Hipp, C. Company Value with Ruin Constraint in a Discrete Model. Preprints 2017, 2017120050 (doi: 10.20944/preprints201712.0050.v1). Hipp, C. Company Value with Ruin Constraint in a Discrete Model. Preprints 2017, 2017120050 (doi: 10.20944/preprints201712.0050.v1).

## 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 C., 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 C., 2003). It is based on closed formulas for first entry probabilities and discount factors for the time until first entry (see Hipp C., 2016). 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 (see Hipp C., 2016), Section 2.2.2 does also yield optimal dividend strategies which differ from those in all other methods, and Lagrange gaps are present here. These gaps always exist in De Finetti models, see (see Hipp C., 2017).

## Keywords

stochastic control; optimal dividend payment; ruin probability constraint

## Subject

MATHEMATICS & COMPUTER SCIENCE, Applied Mathematics

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