Universität zu Köln

Brinker, Leonie Violetta ORCID: 0000-0003-2725-1494 and Schmidli, Hanspeter (2022). OPTIMAL DISCOUNTED DRAWDOWNS IN A DIFFUSION APPROXIMATION UNDER PROPORTIONAL REINSURANCE. J. Appl. Probab., 59 (2). S. 527 - 541. CAMBRIDGE: CAMBRIDGE UNIV PRESS. ISSN 1475-6072

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Abstract

A diffusion approximation to a risk process under dynamic proportional reinsurance is considered. The goal is to minimise the discounted time in drawdown; that is, the time where the distance of the present surplus to the running maximum is larger than a given level d > 0. We calculate the value function and determine the optimal reinsurance strategy. We conclude that the drawdown measure stabilises process paths but has a drawback as it also prevents surpassing the initial maximum. That is, the insurer is, under the optimal strategy, not interested in any more profits. We therefore suggest using optimisation criteria that do not avoid future profits.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Brinker, Leonie Violetta UNSPECIFIED orcid.org/0000-0003-2725-1494 UNSPECIFIED Schmidli, Hanspeter UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-660055
DOI:	10.1017/jpr.2021.68
Journal or Publication Title:	J. Appl. Probab.
Volume:	59
Number:	2
Page Range:	S. 527 - 541
Date:	2022
Publisher:	CAMBRIDGE UNIV PRESS
Place of Publication:	CAMBRIDGE
ISSN:	1475-6072
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language PROBABILITY Multiple languages Statistics & Probability Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/66005