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2010 | Buch

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Market-Consistent Actuarial Valuation

verfasst von: Mario V. Wüthrich, Hans Bühlmann, Hansjörg Furrer

Verlag: Springer Berlin Heidelberg

Buchreihe : EAA Series

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

It is a challenging task to read the balance sheet of an insurance company. This derives from the fact that different positions are often measured by different yardsticks. Assets, for example, are mostly valued at market prices whereas liabilities are often measured by established actuarial methods. However, there is a general agreement that the balance sheet of an insurance company should be measured in a consistent way. Market-Consistent Actuarial Valuation presents powerful methods to measure liabilities and assets in a consistent way. The mathematical framework that leads to market-consistent values for insurance liabilities is explained in detail by the authors. Topics covered are stochastic discounting with deflators, valuation portfolio in life and non-life insurance, probability distortions, asset and liability management, financial risks, insurance technical risks, and solvency.

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Inhaltsverzeichnis

Frontmatter

1. Introduction

Abstract

In Chapter 1 we give a general introduction to the current solvency discussion. This includes a description of actual solvency guidelines and a discussion why we are interested in solvency. The general agreement then is that the balance sheet of an insurance company should be measured in a consistent way. This in particular motivates the development of a market-consistent valuation approach for insurance liabilities.

Mario V. Wüthrich, Hans Bühlmann, Hansjörg Furrer

2. Stochastic discounting

Abstract

In Chapter 2 we define a mathematically consistent model for calculating time values of insurance liability cash flows. The key objects are so-called deflators which play the role of stochastic discount factors. Our definition (via deflators) leads in a natural way to market-consistent values which are consistent with the usual financial theory that involves risk neutral valuation. Typically, in financial mathematics the pricing formulas are based on equivalent martingale measures, economists use the notion of state price density processes and actuaries use the terminology of deflators under the real world probability measure. In Chapter 2 we describe these concepts and we give explicit examples.

Mario V. Wüthrich, Hans Bühlmann, Hansjörg Furrer

3. Valuation portfolio in life insurance

Abstract

In Chapter 3 we define the valuation portfolio for a life insurance policy. The valuation portfolio is a portfolio consisting of financial instruments that replicate the insurance liability cash flows. The construction of the valuation portfolio is done with the help of an explicit example. We proceed in two steps: First, we assume that the cash flows have deterministic insurance technical risk, i.e. we have a deterministic mortality table, and only the value of the financial instruments describe a stochastic process. Then, we map the cash flows onto these financial instruments. In the second step, we introduce stochastic mortality rates yielding insurance technical risk. In that case we follow the construction in step 1, but we add loadings for the insurance technical risk coming from the stochastic mortality table. This construction gives us a replicating portfolio (protected against insurance technical risks) in terms of financial instruments.

Mario V. Wüthrich, Hans Bühlmann, Hansjörg Furrer

4. Financial risks

Abstract

In the previous chapter we have defined the valuation portfolio for insurance liability cash flows. This valuation portfolio can be viewed as a replicating portfolio for insurance liabilities in terms of financial instruments. In this chapter we analyze financial risks which come from the fact that the valuation portfolio and the real existing asset portfolio on the asset side of the balance sheet may differ. This then leads to the notion of solvency. Moreover, we discuss the Margrabe option which hedges financial risks and we compare the price of the Margrabe option to the price of target capital as it is typically used in insurance practice.

Mario V. Wüthrich, Hans Bühlmann, Hansjörg Furrer

5. Valuation portfolio in non-life insurance

Abstract

In this chapter we construct the valuation portfolio for a non-life insurance runoff. That is, we study triangular non-life insurance data and based on these data we construct a replicating portfolio in terms of financial instruments. This replicating portfolio (called valuation portfolio) models the outstanding non-life insurance liabilities. We consider two versions of the valuation portfolio, the first version models the expected outstanding insurance liabilities, the second version considers in addition loadings for insurance technical risks. These constructions are based on the chain-ladder claims reserving method and use cumulative payments data for the analysis.

Mario V. Wüthrich, Hans Bühlmann, Hansjörg Furrer

6. Selected Topics

Abstract

We conclude these lecture notes with selected topics and remarks. These selected topics give several ideas for further developments and research that go beyond the presentation of the previous chapters. For example, we treat the claims development result, profit sharing and legal quotes.

Mario V. Wüthrich, Hans Bühlmann, Hansjörg Furrer

Backmatter

Titel: Market-Consistent Actuarial Valuation
verfasst von: Mario V. Wüthrich
Hans Bühlmann
Hansjörg Furrer
Copyright-Jahr: 2010
Verlag: Springer Berlin Heidelberg
Electronic ISBN: 978-3-642-14852-1
Print ISBN: 978-3-642-14851-4
DOI: https://doi.org/10.1007/978-3-642-14852-1

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