Diversified portfolios with jumps in a Benchmark framework

Asia-Pacific Financial Markets

Volumn 11, Issue 1, 2004, Pages 1-22

  Platen, Eckhard ^a  

^a UNIVERSITY OF TECHNOLOGY SYDNEY   (Australia)

Author keywords

Benchmark model; Diversified portfolio; Growth optimal portfolio

Indexed keywords

EID: 23944515507     PISSN: 13872834     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10690-005-4253-8     Document Type: Article

References (37)

1. Ansel, J. P. and Stricker, C. (1994) Couverture des actifs contingents, Ann. Inst. H. Poincaré Probab. Stat. 30, 303-315.
2. Artzner, P. (1997) On the numeraire portfolio. Mathematics of Derivative Securities, Cambridge University Press, Cambridge, pp. 53-58.
3. Bajeux-Besnainou, I. and Portait, R. (1997) The numeraire portfolio: A new perspective on financial theory, Eur. J. Finance 3, 291-309.
4. Basle (1995) Planned Supplement to the Capital Accord to Incorporate Market Risk. Basle Committee on Banking and Supervision, Basle, Switzerland.
5. Becherer, D. (2001) The numeraire portfolio for unbounded semimartingales, Finance Stoch. 5, 327-341.
6. Björk, T. and Näslund, B. (1998) Diversified portfolios in continuous time, Eur. Finance Rev. 1, 361-387.
7. Breymann, W., Kelly, L. and Platen, E. (2004) Intraday Empirical Analysis and Modeling of Diversified World Stock Indices, Technical Report, University of Technology, Sydney, QFRC Research, p. 125.
8. Constatinides, G. M. (1992) A theory of the nominal structure of interest rates, Rev. Financ. Studies 5, 531-552.
9. Delbaen, F. and Schachermayer, W. (1994) A general version of the fundamental theorem of asset pricing, Math. Ann. 300, 463-520.
10. Delbaen, F. and Schachermayer, W. (1998) The fundamental theorem of asset pricing for unbounded stochastic processes, Math. Ann. 312, 215-250.
11. Duffie, D. (2001) Dynamic Asset Pricing Theory (3rd ed.), Princeton University Press, Princeton.
12. Fernholz, E. R. (2002) Stochastic Portfolio Theory, Vol. 48 of Applications of Mathematics, Springer, New York.
13. Föllmer, H. and Schweizer, M. (1991) Hedging of contingent claims under incomplete information. In M. Davis and R. Elliott (eds.), Applied Stochastic Analysis, Vol. 5 of Stochastics Monographs, Gordon and Breach, London/New York, pp. 389-414.
14. Föllmer, H. and Sondermann, D. (1986) Hedging of non-redundant contingent claims. In W. Hildebrandt and A. Mas-Colell (eds.), Contributions to Mathematical Economics, North Holland, pp. 205-223.
15. Goll, T. and Kallsen, J. (2003) A complete explicit solution to the log-optimal portfolio problem, Adv. Appl. Probab. 13(2), 774-799.
16. Guan, L. K., Liu, X. and Chong, T. K. (2004) Asymptotic dynamics and VaR of large diversified portfolios in a jump-diffusion market, Quant. Finance 4(2), 129-139.
17. Harrison, J. M. and Kreps, D. M. (1979) Martingale and arbitrage in multiperiod securities markets, J. Econ. Theory 20, 381-408.
18. Harrison, J. M. and Pliska, S. R. (1981) Martingales and stochastic integrals in the theory of continuous trading, Stochastic Process. Appl. 11(3), 215-260.
19. Heath, D. and Platen, E. (2002) Consistent pricing and hedging for a modified constant elasticity of variance model, Quant. Finance 2(6), 459-467.
20. Heath, D. and Platen, E. (2003) Pricing of index options under a minimal market model with lognormal scaling, Quant. Finance 3(6), 442-450.
21. Hofmann, N. and Platen, E. (2000) Approximating large diversified portfolios, Math. Finance 10(1), 77-88.
22. Karatzas, I. and Shreve, S. E. (1998) Methods of Mathematical Finance, Vol. 39 of Applications of Mathematics, Springer, New York.
23. Kelly, J. R. (1956) A new interpretation of information rate, Bell Syst. Tech. J. 35, 917-926.
24. Kramkov, D. O. and Schachermayer, W. (1999) The asymptotic elasticity of utility functions and optimal investment in incomplete markets, Ann. Appl. Probab. 9, 904-950.
25. Long, J. B. (1990) The numeraire portfolio, J. Financ. Econ. 26, 29-69.
26. Markowitz, H. (1959) Portfolio Selection: Efficient Diversification of Investment, Wiley, New York.
27. Merton, R. C. (1973) An intertemporal capital asset pricing model, Econometrica 41, 867-888.
28. Platen, E. (2001) A minimal financial market model. In Trends in Mathematics, Birkhäuser, pp. 293-301.
29. Platen, E. (2002) Arbitrage in continuous complete markets, Adv. Appl. Probab. 34(3), 540-558.
30. 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, Singapore, pp. 305-335.
31. Platen, E. (2004b) A class of complete benchmark models with intensity based jumps, J. Appl. Probab. 41, 19-34.
32. Platen, E. (2004c) Modeling the volatility and expected value of a diversified world index, Int. J. Theor. Appl. Finance 7(4), 511-529.
33. Platen, E. and Stahl, G. (2003) A structure for general and specific market risk, Comput. Statist. 18(3), 355-373.
34. Protter, P. (1990). Stochastic Integration and Differential. Equations, Springer, Berlin.
35. Rogers, L. C. G. (1997) The potential approach to the term structure of interest rates and their exchange rates, Math. Finance 7, 157-176.
36. Ross, S. A. (1976) The arbitrage theory of capital asset pricing, J. Econ. Theory 13, 341-360.
37. Sharpe, W. F. (1964) Capital asset prices: A theory of market equilibrium under conditions of risk, J. Finance 19, 425-442.