Continuous-time mean-variance portfolio selection with bankruptcy prohibition

A continuous-time mean-variance portfolio selection problem is studied where all the market coefficients are random and the wealth process under any admissible trading strategy is not allowed to be below zero at any time. The trading strategy under consideration is defined in terms of the dollar amounts, rather than the proportions of wealth, allocated in individual stocks. The problem is completely solved using a decomposition approach. Specifically, a (constrained) variance minimizing problem is formulated and its feasibility is characterized. Then, after a system of equations for two Lagrange multipliers is solved, variance minimizing portfolios are derived as the replicating portfolios of some contingent claims, and the variance minimizing frontier is obtained. Finally, the efficient frontier is identified as an appropriate portion of the variance minimizing frontier after the monotonicity of the minimum variance on the expected terminal wealth over this portion is proved and all the efficient portfolios are found. In the special case where the market coefficients are deterministic, efficient portfolios are explicitly expressed as feedback of the current wealth, and the efficient frontier is represented by parameterized equations. Our results indicate that the efficient policy for a mean-variance investor is simply to purchase a European put option that is chosen, according to his or her risk preferences, from a particular class of options. © 2005 Blackwell Publishing Inc

Aktien

Der Deutsche Aktienindex klettert auf Bestmarken, stürzt wieder ab, erholt sich wieder. Ein Unternehmen macht Rekordgewinne, der Aktienkurs bricht trotzdem ein, weil Analysten noch mehr erwartet hatten. Für den Normalbürger ist das kaum nachvollziehbar. Wie sieht es mit Wirtschaftswissenschaftlern aus? Investieren die in Aktien, oder lassen sie die Finger davon? Ein Gespräch mit Peter Dürsch, Wissenschaftlicher Mitarbeiter am Alfred-Weber-Institut für Wirtschaftswissenschaften der Universität Heidelberg. Der Beitrag erschien in der Sendereihe "Campus-Report" - einer Beitragsreihe, in der über aktuelle Themen aus Forschung und Wissenschaft der Universitäten Heidelberg, Mannheim, Karlsruhe und Freiburg berichtet wird. Zu hören ist "Campus-Report" montags bis freitags jeweils um ca. 19.10h im Programm von Radio Regenbogen. (Empfang in Nordbaden: UKW 102,8. In Mittelbaden: 100,4 und in Südbaden: 101,1

Pricing futures on geometric indexes: A discrete time approach

Several futures contracts are written against an underlying asset that is a geometric, rather than arithmetic, index. These contracts include: the US Dollar Index futures, the CRB-17 futures, and the Value Line geometric index futures. Due to the geometric averaging, the standard cost-of-carry futures pricing formula is improper for pricing these futures contracts. We assume that asset prices are lognormally distributed, and capital markets are complete. Using the concepts of equivalent martingale measure and the risk-neutral valuation relationships in conjunction with discrete time methodology, we derive closed-form pricing formulas for these contracts. Our pricing formulas are consistent with the ones obtained via a continuous time paradigm. Copyright Springer Science+Business Media, LLC 2007Geometric indexes, Futures pricing, Risk-neutral valuation, Discrete time model,