Next Article in Journal
A Simple Traffic Light Approach to Backtesting Expected Shortfall
Previous Article in Journal
A General Framework for Incorporating Stochastic Recovery in Structural Models of Credit Risk
Article Menu
Issue 1 (March) cover image

Export Article

Open AccessArticle

Company Value with Ruin Constraint in a Discrete Model

Karlsruhe Institute of Technology, Karlsruhe 76131, Germany
Received: 6 December 2017 / Revised: 29 December 2017 / Accepted: 4 January 2018 / Published: 7 January 2018
Full-Text   |   PDF [279 KB, uploaded 9 January 2018]   |  

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. View Full-Text
Keywords: stochastic control; optimal dividend payment; ruin probability constraint stochastic control; optimal dividend payment; ruin probability constraint
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
SciFeed

Share & Cite This Article

MDPI and ACS Style

Hipp, C. Company Value with Ruin Constraint in a Discrete Model. Risks 2018, 6, 1.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Risks EISSN 2227-9091 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top