Continuous-time (Ross-type) portfolio separation, (almost) without Itô calculus

Abstract

This paper shows how the distributions-based portfolio separation theorem – also known as the mutual fund theorem – for elliptical and stable distributions carries over from a static to a continuous-time model. Without invoking Itô stochastic calculus, only the definition of the Itô integral, we generalize and simplify an approach of Khanna and Kulldorff (http://link.springer.com/article/10.1007%2Fs007800050056 Finance Stoch. 3 (1999), pp. 167–185). In addition to (re-) covering the classical cases, this paper also gives separation results for non-symmetric stable distributions under no shorting-conditions, including a new case of one fund separation without risk-free opportunity. Applicability of the skewed cases to insurance and banking is discussed, as well as limitations.

Keywords:

• Portfolio separation
• mutual fund theorem
• elliptical distributions
• (Lévy-Pareto) -stable
• Lévy processes
• stochastic dominance
• portfolio constraints
• incomplete markets
• risk management

AMS Subject Classifications:

• 91G10
• 91G80
• 60E07
• 60E15
• 60G50
• 60G51
• 60G52
• 60H05
• 93E20
• 49K45

Acknowledgements

The work was initiated at the Stockholm School of Economics, a stay supported by NorFA; thanks to Tomas Björk for introducing me to the idea and the Khanna/Kulldorff approach. During the research, the author has been affiliated with The Financial Supervisory Authority of Norway; the usual disclaimer applies. The paper has benefited from referee comments. All errors are mine.

Notes

No potential conflict of interest was reported by the author.

Additional information

Funding

This manuscript is based on and contains results from a chapter of the author’s doctoral dissertation, a project supervised by Bernt Øksendal and funded by the Research Council of Norway [grant number 125669].