Abstract
In this chapter we merge all available financial positions to the full balance sheet approach. To avoid inconsistencies it is crucial that the same state price deflator (and valuation method) is applied to all financial positions of the balance sheet. The solvency consideration then adds a dynamic component to the problem, namely, it considers the question whether the values of the liabilities are covered by asset values also in one year’s time from today. We start this chapter by introducing risk measures that analyze the dynamic question under stress scenarios. Then we define the notions of solvency and acceptability which are supplemented by many examples in asset-and-liability management. We discuss the limited liability option of shareholders, provide insight on dividend payment rules. We analyze hedging financial risk with the Margrabe option and we discuss portfolio optimization under solvency constraints.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Acciaio B, Penner I (2011) Dynamic risk measures. In: Di Nunno G, Øksendal B (eds) Advanced mathematical methods for finance. Springer, Berlin, pp 1–34
Acerbi C, Tasche D (2002) On the coherence of expected shortfall. J Bank Finance 26(7):1487–1503
Artzner P, Eisele KT (2010) Supervisory insurance accounting: mathematics for provision- and solvency capital-requirements. ASTIN Bull 40(2):569–585
Artzner P, Delbaen F, Eber JM, Heath D (1997) Thinking coherently. Risk 10(11):68–71
Artzner P, Delbaen F, Eber JM, Heath D (1999) Coherent measures of risk. Math Finance 9(3):203–228
Artzner P, Delbaen F, Koch-Medina P (2009) Risk measures and efficient use of capital. ASTIN Bull 39(1):101–116
Black F, Scholes M (1972) The valuation of option contracts and a test of market efficiency. J Finance 27(2):399–417
Black F, Scholes M (1973) The pricing of options and corporate liabilities. J Polit Econ 81(3):637–654
Dahl M (2007) A discrete-time model for reinvestment risk in bond markets. ASTIN Bull 37(2):235–264
Embrechts P, Nešlehová J, Wüthrich MV (2009) Additivity properties for value-at-risk under Archimedean dependence and heavy-tailedness. Insur Math Econ 44(2):164–169
Filipović D (2009) Term-structure models. A graduate course. Springer, Berlin
Föllmer H, Schied A (2004) Stochastic finance: an introduction in discrete time, 2nd edn. De Gruyter, Berlin
Hilli P, Koivu M, Pennanen T (2011) Cash-flow based valuation of pension liabilities. Eur Actuar J 1(suppl 2):329–343
Ingersoll JE (1987) Theory of financial decision making. Rowman & Littlefield, Lanham
Lamberton D, Lapeyre B (2007) Introduction to stochastic calculus applied to finance, 2nd edn. Chapman & Hall/CRC Press, London/Boca Raton
Ledoit O, Wolf M (2003) Improved estimation of the covariance matrix of stock returns with an application to portfolio selection. J Empir Finance 10:603–621
Ledoit O, Wolf M (2003) Honey, I shrunk the sample covariance matrix. J Portf Manag 30:110–119
Lindskog F (2000) Linear correlation estimation. Working paper. RiskLab, ETH Zürich
Margrabe W (1978) The value of an option to exchange one asset for another. J Finance 33(1):177–186
Markowitz H (1952) Portfolio selection. J Finance 7(1):77–91
McNeil AJ, Frey R, Embrechts P (2005) Quantitative risk management: concepts, techniques and tools. Princeton University Press, Princeton
Pfeiffer R, Bierbaum J, Kunze M, Quapp N, Bäuerle N (2010) Zinsmodelle für Versicherungen—Diskussion der Anforderungen und Vergleich der Modelle von Hull-White und Cairns. Blätter DGVFM 31:261–290
Rockafellar RT, Uryasev S (2000) Optimization of conditional value-at-risk. J Risk 2(3):21–42
Rockafellar RT, Uryasev S (2002) Conditional value-at-risk for general loss distributions. J Bank Finance 26(7):1443–1471
Rogers LCG (1995) Which model for term-structure of interest rates should one use? In: Mathematical finance. IMA, vol 65. Springer, Berlin, pp 93–116
Stefanovits D (2010) Equal contributions to risk and portfolio construction. Master thesis, ETH Zurich
Swiss Solvency Test (2006) FINMA SST technisches Dokument, version 2, October 2006
Wüthrich MV, Bühlmann H, Furrer H (2010) Market-consistent actuarial valuation, 2nd edn. Springer, Berlin
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Wüthrich, M.V., Merz, M. (2013). Solvency. In: Financial Modeling, Actuarial Valuation and Solvency in Insurance. Springer Finance. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31392-9_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-31392-9_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31391-2
Online ISBN: 978-3-642-31392-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)