The goal is to provide a sound theoretical underpinning for results
obtained in recent papers and to develop a unified framework for a non-linear
approach to hedging and pricing of financial derivatives. We examine alternative
formulations of no-arbitrage property for non-linear market models. Valuation of
contracts is examined both from the perspective of the hedger and the counterparty
with arbitrary initial endowments. We derive inequalities for unilateral prices
and we study the range for either fair bilateral prices or bilaterally profitable
prices. The study hinges on results for BSDE driven by continuous martingales.
We also derive the pricing PDEs for path-independent contingent claims of European
style in a Markovian framework.
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