Time-Consistent Actuarial Valuations
Recent 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.
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,"
Wiley Blackwell, vol. 16(1), pages 131-151.
- Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
- Stadje, Mitja, 2010. "Extending dynamic convex risk measures from discrete time to continuous time: A convergence approach," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 391-404, December.
- 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.
- Marek Musiela & Thaleia Zariphopoulou, 2004. "An example of indifference prices under exponential preferences," Finance and Stochastics, Springer, vol. 8(2), pages 229-239, 05.
- Stephen Figlewski & Bin Gao, 1998.
"The Adaptive Mesh Model: A New Approach to Efficient Option Pricing,"
New York University, Leonard N. Stern School Finance Department Working Paper Seires
98-032, New York University, Leonard N. Stern School of Business-.
- Figlewski, Stephen & Gao, Bin, 1999. "The adaptive mesh model: a new approach to efficient option pricing," Journal of Financial Economics, Elsevier, vol. 53(3), pages 313-351, September.
- Jocelyne Bion-Nadal, 2008. "Dynamic risk measures: Time consistency and risk measures from BMO martingales," Finance and Stochastics, Springer, vol. 12(2), pages 219-244, April.
- A. Jobert & L. C. G. Rogers, 2007.
"Valuations and dynamic convex risk measures,"
- 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.
- Goovaerts, Marc J. & Laeven, Roger J.A., 2008. "Actuarial risk measures for financial derivative pricing," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 540-547, April.
- Vicky Henderson, 2002. "Valuation Of Claims On Nontraded Assets Using Utility Maximization," Mathematical Finance, Wiley Blackwell, vol. 12(4), pages 351-373.
- Stadje, M.A. & Pelsser, A., 2014. "Time-Consistent and Market-Consistent Evaluations (Revised version of 2012-086)," Discussion Paper 2014-002, Tilburg University, Center for Economic Research.
- Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
- Amin, Kaushik I, 1993. " Jump Diffusion Option Valuation in Discrete Time," Journal of Finance, American Finance Association, vol. 48(5), pages 1833-1863, December.
- Frank Riedel, 2003.
"Dynamic Coherent Risk Measures,"
03004, Stanford University, Department of Economics.
- Monoyios, Michael, 2004. "Option pricing with transaction costs using a Markov chain approximation," Journal of Economic Dynamics and Control, Elsevier, vol. 28(5), pages 889-913, February.
- Biffis, Enrico, 2005. "Affine processes for dynamic mortality and actuarial valuations," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 443-468, December.
- Yuen, Fei Lung & Yang, Hailiang, 2009. "Option Pricing in a Jump-Diffusion Model with Regime Switching," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 39(02), pages 515-539, November.
- Rainer Baule & Marco Wilkens, 2004. "Lean Trees--A General Approach for Improving Performance of Lattice Models for Option Pricing," Review of Derivatives Research, Springer, vol. 7(1), pages 53-72.
- Hilliard, Jimmy E. & Schwartz, Adam, 2005. "Pricing European and American Derivatives under a Jump-Diffusion Process: A Bivariate Tree Approach," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 40(03), pages 671-691, September.
- Cheridito, Patrick & Stadje, Mitja, 2009. "Time-inconsistency of VaR and time-consistent alternatives," Finance Research Letters, Elsevier, vol. 6(1), pages 40-46, March.
- Berend Roorda & J. M. Schumacher & Jacob Engwerda, 2005. "Coherent Acceptability Measures In Multiperiod Models," Mathematical Finance, Wiley Blackwell, vol. 15(4), pages 589-612.
- Jang, Jiwook, 2007. "Jump diffusion processes and their applications in insurance and finance," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 62-70, July.
- Rosazza Gianin, Emanuela, 2006. "Risk measures via g-expectations," Insurance: Mathematics and Economics, Elsevier, vol. 39(1), pages 19-34, August.
- Merton, Robert C., 1976.
"Option pricing when underlying stock returns are discontinuous,"
Journal of Financial Economics,
Elsevier, vol. 3(1-2), pages 125-144.
- Merton, Robert C., 1975. "Option pricing when underlying stock returns are discontinuous," Working papers 787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
- David Hobson, 2004. "STOCHASTIC VOLATILITY MODELS, CORRELATION, AND THE "q"-OPTIMAL MEASURE," Mathematical Finance, Wiley Blackwell, vol. 14(4), pages 537-556.
- Hua Chen & Samuel H. Cox, 2009. "Modeling Mortality With Jumps: Applications to Mortality Securitization," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(3), pages 727-751.
- Wang, Shaun S., 2002. "A Universal Framework for Pricing Financial and Insurance Risks," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 32(02), pages 213-234, November.
- Mitja Stadje & Antoon Pelsser, 2011.
"Time-Consistent and Market-Consistent Evaluations,"
1109.1749, arXiv.org, revised Dec 2013.
- Patrick Cheridito & Freddy Delbaen & Michael Kupper, 2005. "Coherent and convex monetary risk measures for unbounded càdlàg processes," Finance and Stochastics, Springer, vol. 9(3), pages 369-387, 07.
When requesting a correction, please mention this item's handle: RePEc:arx:papers:1109.1751. See general information about how to correct material in RePEc.
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.