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Approximation and Simulation of Large Diversified Portfolios

Funding: 2003: $70,000
2004: $67,000
2005: $67,000
2006: $20,000

Project Member(s): Platen, E.

Funding or Partner Organisation: Australian Research Council (ARC Discovery Projects)

Start year: 2003

Summary: The measurement of risk for large diversified portfolios, consisting of primary securities and derivatives, will play a key role in future financial technology. Based on a new characterisation of asymptotic portfolios this project proposes the development, implementation and testing of highly efficient new approximate risk measurement methodologies suitable for portfolios with hundreds or thousands of instruments. Comparisons with standard and new simulation methods will demonstrate their superiority. The outcomes of this project will give Australian industry an internationally competitive advantage in the measurement and management of risk for large diversified portfolios such as those of superannuation funds and banks.''

Publications:

Bruti Liberati, N & Platen, E 2007, 'Approximation of Jump Diffusions in Finance and Economics', Computational Economics, vol. 29, no. 3-4, pp. 283-312.
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Bruti Liberati, N & Platen, E 2007, 'Strong Approximations of Stochastic Differential Equations with Jumps', Journal of Computational and Applied Mathematics, vol. 205, no. 2, pp. 982-1001.
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Platen, E & Heath, DP 2006, A Benchmark Approach to Quantitative Finance, 1st, Springer, Berlin, Germany.
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Heath, DP & Platen, E 2006, 'Local volatility function models under a benchmark approach', Quantitative Finance, vol. 6, no. 3, pp. 197-206.
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Platen, E 2006, 'A benchmark approach to finance', Mathematical Finance, vol. 16, no. 1, pp. 131-151.
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Platen, E 2004, 'Capital asset pricing for markets with intensity based jumps', Stochastic Finance, International Conference on Stochastic Finance 2004, Springer, Lisboa, Portugal, pp. 157-182.
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Heath, DP & Platen, E 2005, 'Currency derivatives under a minimal market model with random scaling', International Journal of Theoretical and Applied Finance, vol. 8, no. 8, pp. 1157-1177.
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Heath, DP & Platen, E 2005, 'Understanding the implied volatility surface for options on a diversified index', Asia-Pacific Financial markets, vol. 11, no. 1, pp. 55-77.
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Miller, S & Platen, E 2005, 'A two-factor model for low interest rate regimes', Asia-Pacific Financial Markets, vol. 11, no. 1, pp. 107-133.
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Platen, E 2005, 'An alternative interest rate term structure model', International Journal of Theoretical & Applied Finance, vol. 8, no. 6, pp. 717-735.
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Platen, E 2005, 'Diversified portfolios with jumps in a benchmark framework', Asia-Pacific Financial Markets, vol. 11, no. 1, pp. 1-22.
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Platen, E 2005, 'On the role of the growth optimal portfolio in finance', Australian Economic Papers, vol. 44, no. 4, pp. 365-388.
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Platen, E & Runggaldier, WJ 2005, 'A benchmark approach to filtering in finance', Asia-Pacific Financial Markets, vol. 11, no. 1, pp. 79-105.
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Platen, E & West, JM 2005, 'A fair pricing approach to weather derivatives', Asia-Pacific Financial Markets, vol. 11, no. 1, pp. 23-53.
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Bruti Liberati, N, Platen, E, Martini, F & Piccardi, M 2005, 'A multi-point distributed random variable accelerator for Monte Carlo simulation in finance', Proceedings of 5th International Conference On Intelligent Systems Design And Applications, International Conference on Intelligent Systems Designs and Applications, IEEE, Wroclaw, Poland, pp. 532-537.
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Martini, F, Piccardi, M, Bruti Liberati, N & Platen, E 2005, 'A hardware generator for multi-point distributed random variables', 2005 IEEE International Symposium On Circuits And Systems (Iscas), Vols 1-6, Conference Proceedings, International Symposium on Circuits and Systems, IEEE Computer Society Press, Kobe, Japan, pp. 1702-1705.
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Platen, E 2004, 'Simulation methods for stochastic differential equations' in Teugels, J & Sundt, B (eds), Encyclopedia of Actuarial Science, John Wiley & Sons, Chichester, UK, pp. 1559-1564.

Craddock, MJ & Platen, E 2004, 'Symmetry group methods for fundamental solutions', Journal of Differential Equations, vol. 207, no. 2, pp. 285-302.
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Kelly, L, Platen, E & Sorensen, M 2004, 'Estimation for discretely observed diffusions using transform functions', Journal Of Applied Probability, vol. 41, no. A, pp. 99-118.
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Platen, E 2004, 'A class of complete benchmark models with intensity-based jumps', Journal Of Applied Probability, vol. 41, no. 1, pp. 19-34.
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Platen, E 2004, 'Modeling the volatility and expected value of a diversified world index', International Journal of Theoretical and Applied Finance, vol. 7, no. 4, pp. 511-529.
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Bruti Liberati, N & Platen, E 2004, 'On the efficiency of simplified weak taylor schemes for monte carlo simulation in finance.', Computational Science - ICCS 2004, International Conference on Computational Science, Springer-Verlag, Poland, pp. 771-778.
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Platen, E 2003, 'A benchmark framework for risk management', Proceedings of the Ritsumeikan International Symposium: "Stochastic Processes and Applications to Mathematical Finance", International Symposium on "Stochastic Processes and Applications to Mathematical Finance", World Scientific, Kusatsu, Shiga, Japan, pp. 305-335.
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Platen, E 2003, 'Pricing and hedging for incomplete jump diffusion benchmark models', Mathematics of Finance: Proceedings of an AMS-IMS-SIAM Joint Summer Research Conference on Mathematics of Finance, AMS-IMS-SIAM Joint Summer Research Conference on Mathematics of Finance, American Mathematical Society, Snowbird, Utah, USA, pp. 287-301.
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Platen, E & Stahl, G 2003, 'A structure for general and specific market risk', Computational Statistics, vol. 18, no. 3, pp. 355-373.
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Heath, DP & Platen, E 2003, 'Pricing of index options under a minimal market model with lognormal scaling', Workshop on Mathematical Finance, --, St Johns, Canada.

Keywords: Risk measurement Diversified portfolios Stochastic differential equations Simulation Value at risk Credit risk

FOR Codes: Finance, Stochastic Analysis and Modelling, Finance and investment services