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,
Full paper available on request.