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Sharpe Ratio Maximization and Expected Utility when Asset Prices have Jumps

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Author Info
Morten Christensen (University of Southern Denmark)
Eckhard Platen () (School of Finance and Economics, University of Technology, Sydney)

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Abstract

We analyze portfolio strategies which are locally optimal, meaning that they maximize the Sharpe ratio in a general continuous time jump-diffusion framework. These portfolios are characterized explicitly and compared to utility based strategies. In the presence of jumps, maximizing the Sharpe ratio is shown to be generally inconsistent with maximizing expected utility, but this is shown to depend strongly on market completeness and whether event risk is priced.

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Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 170.

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Length: 27
Date of creation: 01 Nov 2005
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Handle: RePEc:uts:rpaper:170

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  2. James Tobin, 1956. "Liquidity Preference as Behavior Towards Risk," Cowles Foundation Discussion Papers 14, Cowles Foundation, Yale University. [Downloadable!]
  3. Martin Kulldorff & Ajay Khanna, 1999. "A generalization of the mutual fund theorem," Finance and Stochastics, Springer, vol. 3(2), pages 167-185. [Downloadable!] (restricted)
  4. Nielsen, Lars Tyge & Vassalou, Maria, 2004. "Sharpe Ratios and Alphas in Continuous Time," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 39(01), pages 103-114, March. [Downloadable!]
  5. Holger Kraft & Mogens Steffensen, 2005. "How to Invest Optimally in Corporate Bonds: A Reduced-Form Approach," FRU Working Papers 2005/07, University of Copenhagen. Department of Economics. Finance Research Unit. [Downloadable!]
  6. John H. Cochrane & Jesus Saa-Requejo, 1996. "Beyond Arbitrage: "Good-Deal" Asset Price Bounds in Incomplete Markets," NBER Working Papers 5489, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  7. Schweizer, Martin, 1992. "Martingale densities for general asset prices," Journal of Mathematical Economics, Elsevier, vol. 21(4), pages 363-378. [Downloadable!] (restricted)
  8. Morten Christensen & Eckhard Platen, 2004. "A General Benchmark Model for Stochastic Jump Sizes," Research Paper Series 139, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
  9. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December. [Downloadable!] (restricted)
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  10. Back, Kerry, 1991. "Asset pricing for general processes," Journal of Mathematical Economics, Elsevier, vol. 20(4), pages 371-395. [Downloadable!] (restricted)
  11. Eckhard Platen, 2004. "Capital Asset Pricing for Markets with Intensity Based Jumps," Research Paper Series 143, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
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