Ross-type Dynamic Portfolio Separation (almost) without Ito Stochastic Calculus
Nils chr. Framstad
While it is common knowledge that portfolio separation in a continuous-time lognormal market is due to the basic properties of the Gaussian distribution, the usual textbook exposition relies on dynamic programming and thus Itô stochastic calculus and the appropriate regularity conditions. This paper shows how Ross-type distributions-based separation properties in continuous-time and discrete-time models, are easily inherited from a single-period model, generalizing and simplifying an approach of Khanna and Kulldorff (Finance Stoch. 3 (1999), pp. 167–185) down to multivariate distributions theory, stochastic dominance and the definition of the Itô integral. In addition to (re-) covering the classical cases of elliptical distributions (with or without risk-free opportunity) and symmetric α-stables/substables, this paper also gives separation results for non-symmetric stable returns distributions under no shorting-conditions, this including new cases of one fund separation without risk-free opportunity. Applicability of the skewed cases to insurance and banking is discussed, as well as limitations.