Skip to main content
×
×
Home

Dynamic risk measures for stochastic asset processes from ruin theory

  • Yasutaka Shimizu (a1) and Shuji Tanaka (a2)
Abstract

This article considers a dynamic version of risk measures for stochastic asset processes and gives a mathematical benchmark for required capital in a solvency regulation framework. Some dynamic risk measures, based on the expected discounted penalty function launched by Gerber and Shiu, are proposed to measure solvency risk from the company’s going-concern point of view. This study proposes a novel mathematical justification of a risk measure for stochastic processes as a map on a functional path space of future loss processes.

Copyright
Corresponding author
*Correspondence to: Yasutaka Shimizu, Department of Applied Mathematics, Waseda University, Shinjuku-ku, Tokyo 169-8555, Japan. E-mail: shimizu@waseda.jp
References
Hide All
Artzner, P., Delbaen, F., Eber, J. & Heath, D. (1999). Coherent measures of risk. Mathematical Finance, 9(3), 203228.
Artzner, P. & Eisele, K. (2010). Supervisory insurance accounting: mathematics for provision – and solvency capital – requirements. ASTIN Bulletin, 40(2), 569585.
Cheridito, P. & Kupper, M. (2011). Composition of time-consistent dynamic monetary risk measures in discrete time. International Journal of Theoretical and Applied Finance, 14(1), 137162.
Cojocaru, I., Garrido, J. & Zhou, X. (2014). On the finite-time Gerber-Shiu function (Not yet published).
Denuit, M., Dhaene, J., Goovaerts, M. & Kaas, R. (2005). Actuarial Theory for Dependent Risks: Measures, Orders and Models. John Wiley & Sons Ltd, Pondicherry, India.
Eisenberg, J. & Schmidli, H. (2011). Minimising expected discounted capital injections by reinsurance in a classical risk model. Scandinavian Actuarial Journal, 2011(3), 155176.
Feng, R. & Shimizu, Y. (2013). On a generalization from ruin to default in a Lévy insurance risk model. Methodology and Computing in Applied Probability, 15(4), 773802.
Garrido, J. (2010). Five easy pieces on Gerber-Shiu analysis. 3rd International Gerber-Shiu Workshop, University of Waterloo, Ontario, Canada, 14–16 June.
Garrido, J. (2013). Is the finite-time Gerber-Shiu function a risk measure? The 17th International Congress on Insurance: Mathematics and Economics, Copenhagen, Denmark, 1–3 July.
Gerber, H.U. & Loisel, S. (2012). Why ruin theory should be of interest for insurance practitioners and risk managers nowadays? Actuarial and Financial Mathematics, Feb 2012, Bruxelles, Belgium. 17–21.
Gerber, H.U. & Shiu, E.S.W. (1998). On the time value of ruin; with discussion and a reply by the authors. North American Actuarial Journal, 2(1), 4878.
Hardy, M.R. & Wirch, J.L. (2004). The iterated CTE: a dynamic risk measure. North American Actuarial Journal, 8(4), 6275.
Kriele, M. & Wolf, J. (2014). Value-Oriented Risk Management of Insurance Companies. European Actuarial Academy (EAA) Series. Springer, London.
Kuznetsov, A. & Morales, M. (2014). Computing the finite-time expected discounted penalty function for a family of Lévy risk processes. Scandinavian Actuarial Journal, 2014(1), 131.
Loisel, S. & Trufin, J. (2014). Properties of a risk measure derived from the expected area in red. Insurance: Mathematics and Economics, 55, 191199.
Mitric, I.-R. & Trufin, J. (2015). On a risk measure inspired from the ruin probability and the expected deficit at ruin. Scandinavian Actuarial Journal, 2016(10), 932951.
Schmidli, H. (2002). On minimizing the ruin probability by investment and reinsurance. Annals of Applied Probability, 12(3), 890907.
Schmidli, H. (2014). A note on Gerber-Shiu functions with an application. In D. Silvestrov & A. Martin-Löf, (Eds.), Modern Problems in Insurance Mathematics (pp. 2136). Springer, Cham.
Trufin, J., Albrecher, H. & Denuit, M.M. (2011). Properties of a risk measure derived from ruin theory. The Geneva Risk and Insurance Review, 36(2), 174188.
Tsai, C.C. & Willmot, G.E. (2002). A generalized defective renewal equation for the surplus process perturbed by diffusion. Insurance: Mathematics and Economics, 30, 5166.
Wüthrich, M.V. & Merz, M. (2013). Financial Modeling, Actuarial Valuation and Solvency in Insurance. Springer-Verlag, Berlin Heidelberg.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Annals of Actuarial Science
  • ISSN: 1748-4995
  • EISSN: 1748-5002
  • URL: /core/journals/annals-of-actuarial-science
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Keywords

JEL classification

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed