Time-Consistent Actuarial Valuations
AbstractRecent theoretical results establish that time-consistent valuations (i.e. pricing operators) can be created by backward iteration of one-period valuations. In this paper we investigate the continuous-time limits of well-known actuarial premium principles when such backward iteration procedures are applied. We show that the one-period variance premiumprinciple converges to the non-linear exponential indifference valuation. Furthermore, we study the convergence of the one-period standard-deviation principle and establish that the Cost-of-Capital principle, which is widely used by the insurance industry, converges to the same limit as the standard-deviation principle. Finally, we study the connections between our time-consistent pricing operators, Good Deal Bound pricing and pricing under model ambiguity.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1109.1751.
Date of creation: Sep 2011
Date of revision:
Contact details of provider:
Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-09-16 (All new papers)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Eckhard Platen, 2006.
"A Benchmark Approach To Finance,"
Mathematical Finance, Wiley Blackwell,
Wiley Blackwell, vol. 16(1), pages 131-151.
- Eckhard Platen, 2004. "A Benchmark Approach to Finance," Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney 138, Quantitative Finance Research Centre, University of Technology, Sydney.
- Patrick Cheridito & Freddy Delbaen & Michael Kupper, 2005. "Coherent and convex monetary risk measures for unbounded cÃ dlÃ g processes," Finance and Stochastics, Springer, vol. 9(3), pages 369-387, 07.
- Vicky Henderson, 2002. "Valuation Of Claims On Nontraded Assets Using Utility Maximization," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 12(4), pages 351-373.
- Frank Riedel, 2003.
"Dynamic Coherent Risk Measures,"
Working Papers, Stanford University, Department of Economics
03004, Stanford University, Department of Economics.
- Riedel, Frank, 2004. "Dynamic coherent risk measures," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 112(2), pages 185-200, August.
- A. Jobert & L. C. G. Rogers, 2008.
"Valuations And Dynamic Convex Risk Measures,"
Mathematical Finance, Wiley Blackwell,
Wiley Blackwell, vol. 18(1), pages 1-22.
- Berend Roorda & J. M. Schumacher & Jacob Engwerda, 2005. "Coherent Acceptability Measures In Multiperiod Models," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 15(4), pages 589-612.
- Filipovic, Damir & Vogelpoth, Nicolas, 2008. "A note on the Swiss Solvency Test risk measure," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 897-902, June.
- Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 9(3), pages 203-228.
- Rosazza Gianin, Emanuela, 2006. "Risk measures via g-expectations," Insurance: Mathematics and Economics, Elsevier, vol. 39(1), pages 19-34, August.
- Marek Musiela & Thaleia Zariphopoulou, 2004. "An example of indifference prices under exponential preferences," Finance and Stochastics, Springer, vol. 8(2), pages 229-239, 05.
- Freddy Delbaen & Shige Peng & Emanuela Rosazza Gianin, 2010. "Representation of the penalty term of dynamic concave utilities," Finance and Stochastics, Springer, vol. 14(3), pages 449-472, September.
- Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators).
If references are entirely missing, you can add them using this form.