  The research presented in this work is motivated by recent papers by Brigo et
al. (2011), Burgard and Kjaer (2009), Cr\'epey (2012), Fujii and Takahashi
(2010), Piterbarg (2010) and Pallavicini et al. (2012). Our goal is to provide
a sound theoretical underpinning for some results presented in these papers by
developing a unified framework for the non-linear approach to hedging and
pricing of OTC financial contracts. We introduce a systematic approach to
valuation and hedging in nonlinear markets, that is, in markets where cash
flows of the financial contracts may depend on the hedging strategies. Our
systematic approach allows to identify primary sources of and quantify various
adjustment to valuation and hedging, primarily the funding and liquidity
adjustment and credit risk adjustment. We propose a way to define no-arbitrage
in such nonlinear markets, and we provide conditions that imply absence of
arbitrage in some specific market trading models. Accordingly, we formulate a
concept of no-arbitrage price, and we provide relevant (non-linear) BSDE that
produces the no-arbitrage price in case when the contract's cash flows can be
replicated.
