Abstract
The financial market faces risks arising from many types of uncertain losses, including market risk, credit risk, liquidity risk, operational risk, etc. In 1988, the Basel Committee on Banking Supervision proposed measures to control credit risk in banking. A risk measure called the value-at-risk, acronym VaR, became, in the 1990s, an important tool of risk assessment and management for banks, securities companies, investment funds, and other financial institutions in asset allocation and performance evaluation. The VaR associated with a given confidence level for a venture capital is the upper limit of possible losses in the next certain period of time. In 1996 the Basel Committee on Banking Supervision endorsed the VaR as one of the acceptable methods for the bank’s internal risk measure. However, due to the defects of VaR, a variety of new risk measures came into being. This chapter focuses on the representation theorems for static risk measures. For an overview of the subject we refer to Song and Yan (2009b).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Artzner, P., Delbaen, F., Eber, J.M., Heath, D.: Thinking coherently. Risk 10, 68–71 (1997)
Artzner, P., Delbaen, F., Eber, J.M., Heath, D.: Coherent measures of risk. Math. Financ. 9(3), 203–228 (1999)
Choquet, G.: Theory of capacities. Ann. Inst. Fourier Grenoble. 5, 131–295 (1953–54)
Dana, R.-A.: A representation result for concave Schur concave functions. Math. Financ. 15, 615–634 (2005)
Denneberg, D.: Non-additive Measure and Integral. Kluwer Academic, Boston (1994)
Dhaene, J., Vanduffel, S., Goovaerts, M.J., Kaas, R., Tang, Q., Vyncke, D.: Risk measures and comotononicity: a review. Stoch. Model. 22, 573–606 (2006)
Embrechts, P., McNeil, A.J., Straumann, D.: Correlation and dependence in risk management: properties and pitfalls. In: Dempster, M., Moffatt, H.K. (eds.) Risk Management: Value at Risk and Beyond. Cambridge University Press, Cambridge (2000)
Föllmer, H., Schied, A.: Convex measures of risk and trading constraints. Financ. Stoch. 6(4), 429–447 (2002)
Föllmer, H., Schied, A.: Stochastic Finance, an Introduction in Discrete Time, 2nd revised and extended edition. Welter de Gruyter, Berlin, New York (2004)
Frittelli, M., Gianin, E.R.: Putting order in risk measures. J. Bank. Financ. 26(7), 1473–1486 (2002)
Heyde, C.C., Kou, S.G., Peng, X.H.: What is a good risk measure: bridging the gaps between data, coherent risk measure, and insurance risk measure. Preprint (2006)
Kusuoka, S.: On law invariant coherent risk measures. Adv. Math. Econ. 3, 83–95 (2001)
Song, Y., Yan, J.A.: The representations of two types of functionals on \(L^\infty (\varOmega , {\cal F})\) and \(L^\infty (\varOmega , {\cal F}, P)\). Sci. China, Ser. A Math. 49(10), 1376–1382 (2006)
Song, Y., Yan, J.A.: Risk measures with co-monotonic subadditivity or convexity and respecting stochastic orders. Insur. Math. Econ. 45, 459–465 (2009a)
Yan, J.A.: A short presentation of Choquet integral. In: Duan, J. et al., (eds.) Recent Development in Stochastic Dynamics and Stochastic Analysis. Interdisciplinary Mathematical Science, vol. 8, pp. 269–291. Wold Scientific, New Jersey (2010)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Singapore Pte Ltd. and Science Press
About this chapter
Cite this chapter
Yan, JA. (2018). Static Risk Measures. In: Introduction to Stochastic Finance. Universitext. Springer, Singapore. https://doi.org/10.1007/978-981-13-1657-9_10
Download citation
DOI: https://doi.org/10.1007/978-981-13-1657-9_10
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-13-1656-2
Online ISBN: 978-981-13-1657-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)