Skip to main content
Erschienen in: European Actuarial Journal 2/2011

01.07.2011 | Original Research Paper

Cash-flow based valuation of pension liabilities

verfasst von: Petri Hilli, Matti Koivu, Teemu Pennanen

Erschienen in: European Actuarial Journal | Sonderheft 2/2011

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

This paper presents a computational framework for cash-flow based valuation of insurance liabilities in incomplete markets. It accounts for the risks associated with both insurance claims and investment returns until maturity in accordance with modern principles of asset-liability management. The valuation framework is market consistent in the sense that it takes into account the investment opportunities available to the insurer at the time of valuation. The framework is easily adapted to different lines of insurance and it can effectively employ advanced tools for strategic portfolio management. As an application, we value the insurance portfolio of the Finnish private sector occupational pension system where the liabilities extend over 82 years.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Fußnoten
1
Some studies have suggested the use of so called “risk neutral measures” (see e.g. Wüthrich et al. [21]) but in realistic market models, the specification of a risk neutral measure can be a difficult task. Even if feasible, one would still face the choice among the infinitely many risk neutral measures that exist in incomplete markets.
 
2
The Value at Risk at confidence level δ ∈ [0, 1], V@R δ(V T ) is defined as the negative of the (1 − δ)-quantile of V T . The Conditional Value at Risk at confidence level δ is defined as the conditional expectation CV@R δ(V T ) =  − E[V T | V T  ≤  − V@R δ(V T )].
 
Literatur
2.
3.
Zurück zum Zitat Biström K, Elo P, Klaavo T, Risku I, Sihvonen H (2007) Lakisääteiset eläkkeet, pitkänaikavälin laskelmat 2075. Eläketurvakeskuksen raportteja, Eläketurvakeskus Biström K, Elo P, Klaavo T, Risku I, Sihvonen H (2007) Lakisääteiset eläkkeet, pitkänaikavälin laskelmat 2075. Eläketurvakeskuksen raportteja, Eläketurvakeskus
4.
Zurück zum Zitat Black F, Perold AF (1992) Theory of constant proportion portfolio insurance. J Econ Dyn Control 16:403–426MATHCrossRef Black F, Perold AF (1992) Theory of constant proportion portfolio insurance. J Econ Dyn Control 16:403–426MATHCrossRef
5.
Zurück zum Zitat Black F, Scholes M (1973) The pricing of options and corporate liabilities. J Political Econ. 81(3):637–654CrossRef Black F, Scholes M (1973) The pricing of options and corporate liabilities. J Political Econ. 81(3):637–654CrossRef
6.
Zurück zum Zitat Bowers NL, Gerber HU, Hickman JC, Jones DA, Nesbitt CJ (1997) Actuarial Mathematics. In: Shaumburg IL (ed) Society of Actuaries, 2nd edn, ISBN 0-9389594-6-8 Bowers NL, Gerber HU, Hickman JC, Jones DA, Nesbitt CJ (1997) Actuarial Mathematics. In: Shaumburg IL (ed) Society of Actuaries, 2nd edn, ISBN 0-9389594-6-8
7.
Zurück zum Zitat Bühlmann H (1970) Mathematical methods in risk theory. Die Grundlehren der mathematischen Wissenschaften, Band 172. Springer, New York Bühlmann H (1970) Mathematical methods in risk theory. Die Grundlehren der mathematischen Wissenschaften, Band 172. Springer, New York
8.
Zurück zum Zitat Ernst, Young (2008) The meaning of market consistency in Europe Ernst, Young (2008) The meaning of market consistency in Europe
9.
Zurück zum Zitat Föllmer H, Schied A (2004) Stochastic finance. An introduction in discrete time. volume 27 of de Gruyter Studies in Mathematics. Walter de Gruyter & Co., Berlin, extended edition, ISBN 3-11-018346-3 Föllmer H, Schied A (2004) Stochastic finance. An introduction in discrete time. volume 27 of de Gruyter Studies in Mathematics. Walter de Gruyter & Co., Berlin, extended edition, ISBN 3-11-018346-3
10.
Zurück zum Zitat Hilli P, Koivu M, Pennanen T (2007) A stochastic model for assets and liabilities of a pension institution, 2nd PBSS Section Colloquium Hilli P, Koivu M, Pennanen T (2007) A stochastic model for assets and liabilities of a pension institution, 2nd PBSS Section Colloquium
11.
Zurück zum Zitat Hilli P, Koivu M, Pennanen T (2008) Financial Risk Management in the Statutory Occupational Pension System. 2008:19. Reports of the Ministry of Social Affairs and Health (in Finnish) Hilli P, Koivu M, Pennanen T (2008) Financial Risk Management in the Statutory Occupational Pension System. 2008:19. Reports of the Ministry of Social Affairs and Health (in Finnish)
12.
Zurück zum Zitat Hilli P, Koivu M, Pennanen T Optimal construction of a fund of funds. Eur Actuar J (this issue) Hilli P, Koivu M, Pennanen T Optimal construction of a fund of funds. Eur Actuar J (this issue)
13.
Zurück zum Zitat International Association of Insurance Supervisors (2007) The IAIS common structure for the assessment of insurer solvency. Structure paper International Association of Insurance Supervisors (2007) The IAIS common structure for the assessment of insurer solvency. Structure paper
14.
Zurück zum Zitat Jorion P (1997) Value at Risk, the New Benchmark for Controlling Market Risk. McGraw-Hill Jorion P (1997) Value at Risk, the New Benchmark for Controlling Market Risk. McGraw-Hill
16.
Zurück zum Zitat Koivu M, Pennanen T, Ranne A (2005) Modeling assets and liabilities of a Finnish pension insurance company: a VEqC approach. Scand Actuar J (1):46–76 ISSN 0346-1238 Koivu M, Pennanen T, Ranne A (2005) Modeling assets and liabilities of a Finnish pension insurance company: a VEqC approach. Scand Actuar J (1):46–76 ISSN 0346-1238
17.
18.
Zurück zum Zitat Rockafellar RT (2007) Coherent approaches to risk in optimization under uncertainty. In: Gray P, Klastorin T (eds) Tutorials in Operations Research. INFORMS, pp 38–61 Rockafellar RT (2007) Coherent approaches to risk in optimization under uncertainty. In: Gray P, Klastorin T (eds) Tutorials in Operations Research. INFORMS, pp 38–61
19.
Zurück zum Zitat Rockafellar RT, Uryasev SP (2000) Optimization of conditional value-at-risk. J Risk 2:21–42 Rockafellar RT, Uryasev SP (2000) Optimization of conditional value-at-risk. J Risk 2:21–42
20.
Zurück zum Zitat Savela V (2008) Työeläkerahastojen sijoitusrakenne 31.12.2009. TELA Savela V (2008) Työeläkerahastojen sijoitusrakenne 31.12.2009. TELA
21.
Zurück zum Zitat Wüthrich MV, Bühlmann H, Furrer H (2008) Market-consistent actuarial valuation, Springer Wüthrich MV, Bühlmann H, Furrer H (2008) Market-consistent actuarial valuation, Springer
Metadaten
Titel
Cash-flow based valuation of pension liabilities
verfasst von
Petri Hilli
Matti Koivu
Teemu Pennanen
Publikationsdatum
01.07.2011
Verlag
Springer-Verlag
Erschienen in
European Actuarial Journal / Ausgabe Sonderheft 2/2011
Print ISSN: 2190-9733
Elektronische ISSN: 2190-9741
DOI
https://doi.org/10.1007/s13385-011-0023-3

Weitere Artikel der Sonderheft 2/2011

European Actuarial Journal 2/2011 Zur Ausgabe