A Benchmark approach to finance

Mathematical Finance

Volumn 16, Issue 1, 2006, Pages 131-151

  Platen, Eckhard ^a  

^a UNIVERSITY OF TECHNOLOGY SYDNEY   (Australia)

Author keywords

Benchmark model; Capital asset pricing model; Efficient frontier; Fair pricing; Growth optimal portfolio; Market portfolio; Minimal market model; Stochastic volatility

Indexed keywords

EID: 28844444246     PISSN: 09601627     EISSN: 14679965     Source Type: Journal    
DOI: 10.1111/j.1467-9965.2006.00265.x     Document Type: Conference Paper

References (41)

1. ARTZNER, P. (1997): On the Numeraire Portfolio, in Mathematics of Derivative Securities, Cambridge University Press, 53-58.
2. BAJEUX-BESNAINOU, I., and R. PORTAIT (1997): The Numeraire Portfolio: A New Perspective on Financial Theory, The European Journal of Finance 3, 291-309.
3. BECHERER, D. (2001): The Numeraire Portfolio for Unbounded Semimartingales, Finance Stoch. 5, 327-341.
4. BREIMAN, L. (1961): Optimal Gambling Systems for Favorable Games, in Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Volume I, 65-78.
5. BÜHLMANN, H. (1995): Life Insurance with Stochastic Interest Rates, in Financial Risk and Insurance, G. Ottaviani, ed. Springer, 1-24.
6. CHRISTENSEN, M. M., and K. LARSEN (2004): No Arbitrage and the Growth Optimal Portfolio. Technical report, Syddansk University, Denmark. Working paper No. 03/2004.
7. CHRISTENSEN, M. M., and E. PLATEN (2004): A General Benchmark Model for Stochastic Jump Sizes. Technical report, University of Technology, Sydney. QFRC Research Paper 139, to appear in Stochastic Analysis and Applications.
8. COCHRANE, J. H. (2001): Asset Pricing. Princeton University Press.
9. CONSTATINIDES, G. M. (1992): A Theory of the Nominal Structure of Interest Rates, Rev. Finan. Studies 5, 531-552.
10. DELBAEN, F., and W. SCHACHERMAYER (1994): A General Version of the Fundamental Theorem of Asset Pricing, Math. Ann. 300, 463-520.
11. DELBAEN, F., and W. SCHACHERMAYER (1998): The Fundamental Theorem of Asset Pricing for Unbounded Stochastic Processes, Math. Ann. 312, 215-250.
12. DIMSON, E., P. MARSH, and M. STAUNTON (2002): Triumph of the Optimists: 101 Years of Global Investment Returns. Princeton University Press.
13. DUFFIE, D. (2001): Dynamic Asset Pricing Theory, 3rd edition. Princeton University Press.
14. FERGUSSON, K., and E. PLATEN (2005): On the Distributional Characterization for Log-return of a World Stock Index. University of Technology, Sydney, QFRC research paper 153. (Forth-coming in Applied Mathematical Finance).
15. FÖLLMER, H., and M. SCHWEIZER (1991): Hedging of Contingent Claims under Incomplete Information, in Applied Stochastic Analysis, M. Davis and R. Elliott, eds. Volume 5 of Stochastics Monogr. London/New York: Gordon and Breach, 389-414.
16. GEMAN, S., N. EL KAROUI, and J. C. Rochet (1995): Changes of Numeraire, Changes of Probability Measures and Pricing of Options, J. Appl. Probab. 32, 443-458.
17. GERBER, H. U. (1990): Life Insurance Mathematics. Berlin: Springer.
18. GOLL, T., and J. KALLSEN (2003): A Complete Explicit Solution to the Log-Optimal Portfolio Problem, Am. Appl. Probab. 13(2), 774-799.
19. HARRISON, J. M., and D. M. KREPS (1979): Martingale and Arbitrage in Multiperiod Securities Markets, J. Economic. Theory 20, 381-408.
20. HARRISON, J. M., and S. R. PLISKA (1981): Martingales and Stochastic Integrals in the Theory of Continuous Trading, Stochastic Process. Appl. 11(3), 215-260.
21. HEATH, D., and E. PLATEN (2004): Understanding the Implied Volatility Surface for Options on a Diversified Index. Asia-Pacific Financial Markets 11(1), 55-77.
22. 1-Statistical Procedures and Related Topics, Volume 31 of, IMS Lecture Notes - Monograph Series, Y. Dodge, ed. California: Institute of Mathematical Statistics Hayward. 301-314.
23. KARATZAS, I., and S. E. SHREVE (1991): Brownian Motion and Stochastic Calculus, 2nd edition. Springer.
24. KARATZAS, I., and S. E. SHREVE (1998): Methods of Mathematical Finance, Volume 39 of Appl. Math. Springer.
25. KELLY, J. R. (1956): A New Interpretation of Information Rate, Bell Syst. Techn. J. 35, 917-926.
26. KRAMKOV, D. O., and W. SCHACHERMAYER (1999): The Asymptotic Elasticity of Utility Functions and Optimal Investment in Incomplete Markets, Ann. Appl. Probab. 9, 904-950.
27. LATANÉ, H. (1959): Criteria for Choice among Risky Ventures, J. Political Economy 38, 145-155.
28. LINTNER, J. (1965): The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets, Rev. Econom. Statist. 47, 13-37.
29. LONG, J. B. (1990): The Numeraire Portfolio, J. Financial Economics 26, 29-69.
30. MARKOWITZ, H. (1959): Portfolio Selection: Efficient Diversification of Investment. New York: Wiley.
31. MARKOWITZ, H., and N. USMEN (1996): The Likelihood of Various Stock Market Return Distributions, Part 1: Principles of inference, J. Risk Uncertainty 13, 207-219.
32. MERTON, R. C. (1973): An Intertemporal Capital Asset Pricing Model, Econometrica 41, 867-888.
33. PLATEN, E. (2001): A Minimal Financial Market Model, in Trends in Mathematics. Birkhäuser, 293-301.
34. PLATEN, E. (2002): Arbitrage in Continuous Complete Markets, Adv. in Appl. Probab. 34(3), 540-558.
35. PLATEN, E. (2004a): A Benchmark Framework for Risk Management, in Stochastic Processes and Applications to Mathematical Finance, Proceedings of the Ritsumeikan International Symposium: World Scientific, 305-335.
36. PLATEN, E. (2004b): Modeling the Volatility and Expected Value of a Diversified World Index, Int. J. Theor. Appl. Finance 7(4), 511-529.
37. PLATEN, E. (2004c): Pricing and Hedging for Incomplete Jump Diffusion Benchmark Models, in Mathematics of Finance, Volume 351 of Contemporary Mathematics, American Mathematical Society, 287-301.
38. REVUZ, D., and M. YOR (1999): Continuous Martingales and Brownian Motion, 3rd edition. Springer.
39. ROGERS, L. C. G. (1997): The Potential Approach to the Term Structure of Interest Rates and Their Exchange Rates, Math. Finance 7, 157-176.
40. Ross, S. A. (1976): The Arbitrage Theory of Capital Asset Pricing, J. Econ. Theo. 13, 341-360.
41. SHARPE, W. F. (1964): Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk, J. Finan. 19, 425-442.