An Estimation Procedure for Parameters in Segmentation

Segmentation of Portfolios


Scientific Essay, 2009

12 Pages


Excerpt


An Estimation Procedure for Parameters in Segmentation

(Dr. Burkhard Disch, Schwetzingen / Germany)

Abstract

In practice, the actuarial valuation of a stock or an available inventory for new business target market segmentation plays a prominent role, so the formation of sub-stocks to sociological, demographic, geographic or other to be deemed as a corporate-policy relevant criteria. The main problem is to answer the question how great the stock shares for the respective segments are and what the ratios between the termination probabilities are. While estimating the termination probabilities is relatively simple and - with restrictions - can be reliably estimated from external statistics, the stock distribution is highly dependent on the individual company's situation.

What is often known, however, is the affiliation to one segment in the case of termination, when a questionnaire, a special test or a medical examination can be carried out. If there are enough termination cases verifiable, we show that a detailed knowledge of the segmentation of the portfolio to determine the number of terminations is not necessary. The actuarial approach to this is the fact that at any given time and portfolio with a number of termination cases, only the distribution of the number of termination cases in the segments is necessary to determine the individual component units, not the exact number of risks within the (sub-) segments. To calculate this, we determine a division of a given stock portfolio, as we estimate the parameters of segmentation - and calculate the portfolio shares in respect of such subdivision.

The parameters solves some best approximation-criteria. We show this criteria and give the solution of the approximationproblem in some special cases with examples for application. We do this in the deterministic and the stochastic case. We calculate the volume of payments in the different segments by applicating the parameters.

Keywords

Segmentation, life insurance stocks, number of termination cases, approximation, parameters of segmentation, termination probabilities, smoker / non-smoker tariffs, tariff differentiation by occupation, profile of the stock distribution, stochastic analysis

Introduction

In practice, the actuarial valuation of a stock or an available inventory for new business target market segmentation plays a prominent role, so the formation of sub-stocks to sociological, demographic, geographic or other to be deemed as a corporate-policy relevant criteria. For example, for determining the SCR in Solvency models in assessing the impact of risk assessments (selection at the beginning) or differentiated tariffs (smoker / non-smoker tariffs) the methodology used in the formation of sub-stocks is considered substantial input. The main problem is to answer the question how great the stock shares for the respective segments are and what the ratios between the termination probabilities are. While estimating the termination probabilities is relatively simple and - with restrictions - can be reliably estimated from external statistics, the stock distribution is highly dependent on the individual company's situation.

A major problem in answering the question consists in the fact that for an arbitrary stock of policies the percentage of smoker / non-smoker is a priori well known only in rare cases. The proportion of smokers / non-smokers is in fact known - more generally, the mortality ratios are known at least by estimation, but the stock allocation to the individual segments (segmentation of the stock) is unknown. That is the case especially when medical criteria (medical history / pre-existing conditions), socio-economic or geographic criteria is the segmentation-criteria. The mortality relations of smokers to non-smokers can indeed be well estimated, but the proportion of smokers of a given target group or the new business is unknown and therefore the number of indemnifications for smokers is unknown as well.

What is often known, however, is the affiliation to one segment in the case of termination, when a questionnaire, a Cotinintest or a medical examination can be carried out, possibly for only a part of the termination cases. In the case there are enough termination cases (statistically significant number) verifiable, we show below that a detailed knowledge of the segmentation of the portfolio to determine the number of terminations is not necessary. The actuarial approach to this is the fact that at any given time and portfolio with a number of termination cases, only the distribution of the number of termination cases in the segments is necessary to determine the individual component units, not the exact number of risks within the (sub-) segments. To calculate this, we determine a (pseudo-) division of a given stock portfolio, as we estimate the parameters of segmentation - and calculate the portfolio shares in respect of such subdivision. To this end, we make the following general specifications.

In case of a portfolio of (stochastically independent) risks associated with the number A and a (proposed) segmentation, performance probability (relative frequency) q is given by the number of benefit cases Y within a given period of time through Abbildung in dieser Leseprobe nicht enthalten (for the following statements we use the notation “benefit” for “termination”, because we assume that the insurance ends with paying the benefit). The Y benefit cases consist of termination cases Abbildung in dieser Leseprobe nicht enthalten in the segments k with i = 1, ..., k by Abbildung in dieser Leseprobe nicht enthalten. It is not relevant here how the numbers of A and Y are determined (we refer this to the relevant literature [1]). It is interesting for the investigation how the Abbildung in dieser Leseprobe nicht enthalten can be determined by a given A and Y.

[...]

Excerpt out of 12 pages

Details

Title
An Estimation Procedure for Parameters in Segmentation
Subtitle
Segmentation of Portfolios
Author
Year
2009
Pages
12
Catalog Number
V151554
ISBN (eBook)
9783640632404
ISBN (Book)
9783640632718
File size
440 KB
Language
English
Notes
Erweiterung und Übersetzung eines Artikels in "Der Aktuar" (2009)
Keywords
Segmentation, life insurance stocks, number of termination cases, approximation, parameters of segmentation, termination probabilities, smoker / non-smoker tariffs, tariff differentiation by occupation, profile of the stock distribution, stochastic analysis
Quote paper
Dr. Burkhard Disch (Author), 2009, An Estimation Procedure for Parameters in Segmentation, Munich, GRIN Verlag, https://www.grin.com/document/151554

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