A strategy π satisfying (1.1) is called a hedging strategy for H and it is well known that it exists if x is greater than the price of H. In the opposite case each trading strategy is able to hedge the claim at most partially, i.e.
arXiv
Thursday, March 06, 2014
Hedging Problem
Let us briefly sketch the classical hedging problem in a stochastic model of financial market. The goal of an investor having an initial capital x ≥ 0 is to hedge dynamically a given random variable H which represents the payoff of a financial contract at some future date T > 0. He is looking for a trading strategy π such that the related portfolio wealth 
at T exceeds H almost surely, i.e.
%3D1&chs=&chf=&chco=)
(1.1)
A strategy π satisfying (1.1) is called a hedging strategy for H and it is well known that it exists if x is greater than the price of H. In the opposite case each trading strategy is able to hedge the claim at most partially, i.e.%5Clt%201&chs=&chf=&chco=)
, and hence generates the shortfall %5E%2B&chs=&chf=&chco=)
which is strictly positive with positive probability. The related shortfall risk which appears in that case should be minimized to protect the investor against the loss resulting from a low value of the portfolio.
arXiv
A strategy π satisfying (1.1) is called a hedging strategy for H and it is well known that it exists if x is greater than the price of H. In the opposite case each trading strategy is able to hedge the claim at most partially, i.e.
arXiv
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