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Gain-loss pricing under ambiguity of measure

Mustafa Ç. Pınar — 2010

ESAIM: Control, Optimisation and Calculus of Variations

Motivated by the observation that the gain-loss criterion, while offering economically meaningful prices of contingent claims, is sensitive to the reference measure governing the underlying stock price process (a situation referred to as ambiguity of measure), we propose a gain-loss pricing model robust to shifts in the reference measure. Using a dual representation property of polyhedral risk measures we obtain a one-step, gain-loss criterion based theorem of asset pricing under ambiguity of...

On semidefinite bounds for maximization of a non-convex quadratic objective over the unit ball

Mustafa Ç. PinarMarc Teboulle — 2006

RAIRO - Operations Research

We consider the non-convex quadratic maximization problem subject to the unit ball constraint. The nature of the norm structure makes this problem extremely hard to analyze, and as a consequence, the same difficulties are encountered when trying to build suitable approximations for this problem by some tractable convex counterpart formulations. We explore some properties of this problem, derive SDP-like relaxations and raise open questions.

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