Title: Gain-Loss Based Convex Risk Limits in Discrete-Time Trading
Authors: M.C. Pinar


We present an approach for pricing and hedging in incomplete markets, which encompasses other recently introduced approaches for the same purpose. Larsen et al. characterized the set of random variables that can be traded continuously to acceptability at a fixed future date according to a convex risk criterion. This criterion is defined as the expected value at the fixed future date of the wealth process accumulated through trading exceeding certain predefined thresholds under several measures. 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 positions which can be traded in discrete time to acceptability, which specializes to the case of Larsen et al. for a specific choice of the risk aversion parameter and to a robust version of the gain-loss measure of Bernardo and Ledoit 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 a numerical example from option pricing. Key words: Incomplete markets, acceptability, martingale measure, contingent claim, pricing.

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