Continuous-time (Ross-type) portfolio separation, (almost) without Itô calculus
Nils Christian Framstad
Stochastics: An International Journal of Probability and Stochastic Processes, Volume 89, Issue 1, pp. 38-64, 2017
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.