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A NEYMAN-PEARSON PERSPECTIVE ON OPTIMAL REINSURANCE WITH CONSTRAINTS

Published online by Cambridge University Press:  18 January 2017

Ambrose Lo
Ambrose Lo*
Affiliation:
Department of Statistics and Actuarial Science, The University of Iowa, 241 Schaeffer Hall, Iowa City, IA 52242-1409, USA, Tel.: (319) 335-1915
*
E-Mail: ambrose-lo@uiowa.edu
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Abstract

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The formulation of optimal reinsurance policies that take various practical constraints into account is a problem commonly encountered by practitioners. In the context of a distortion-risk-measure-based optimal reinsurance model without moral hazard, this article introduces and employs a variation of the Neyman–Pearson Lemma in statistical hypothesis testing theory to solve a wide class of constrained optimal reinsurance problems analytically and expeditiously. Such a Neyman–Pearson approach identifies the unit-valued derivative of each ceded loss function as the test function of an appropriate hypothesis test and transforms the problem of designing optimal reinsurance contracts to one that resembles the search of optimal test functions achieved by the classical Neyman–Pearson Lemma. As an illustration of the versatility and superiority of the proposed Neyman–Pearson formulation, we provide complete and transparent solutions of several specific constrained optimal reinsurance problems, many of which were only partially solved in the literature by substantially more difficult means and under extraneous technical assumptions. Examples of such problems include the construction of the optimal reinsurance treaties in the presence of premium budget constraints, counterparty risk constraints and the optimal insurer–reinsurer symbiotic reinsurance treaty considered recently in Cai et al. (2016).

Keywords

Distortion1-LipschitzValue-at-Riskreciprocal reinsurancesigned measure
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 47 , Issue 2 , May 2017 , pp. 467 - 499
Copyright
Copyright © Astin Bulletin 2017 

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