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

摘要

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 Ito stochastic calculus, only the definition of the Ito 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.