Gain–loss based convex risk limits in discrete‐time trading

Gain–loss based convex risk limits in discrete‐time trading

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Article ID: iaor20116863
Volume: 8
Issue: 3
Start Page Number: 299
End Page Number: 321
Publication Date: Aug 2011
Journal: Computational Management Science
Authors:
Keywords: risk
Abstract:

We present an approach for pricing and hedging in incomplete markets, which encompasses other recently introduced approaches for the same purpose. In a discrete time, finite space probability framework conducive to numerical computation we introduce a gain–loss ratio based restriction controlled by a loss aversion parameter, and characterize portfolio values which can be traded in discrete time to acceptability. The new risk measure specializes to a well‐known risk measure (the Carr–Geman–Madan risk measure) for a specific choice of the risk aversion parameter, and to a robust version of the gain–loss measure (the Bernardo–Ledoit proposal) for a specific choice of thresholds. The result implies potentially tighter price bounds for contingent claims than the no‐arbitrage price bounds. We illustrate the price bounds through numerical examples from option pricing.

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