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Hedging of the European option in discrete time under transaction costs depending on time

Marek Andrzej Kociński — 2010

Applicationes Mathematicae

Hedging of the European option in a discrete time financial market with proportional transaction costs is considered. It is shown that for a certain class of options the set of portfolios which allow the seller to pay the claim of the buyer in quite a general discrete time market model is the same as the set of such portfolios under the assumption that the stock price movement is given by a suitable CRR model.

The martingale method of shortfall risk minimization in a discrete time market

Marek Andrzej Kociński — 2012

Applicationes Mathematicae

The shortfall risk minimization problem for the investor who hedges a contingent claim is studied. It is shown that in case the nonnegativity of the final wealth is not imposed, the optimal strategy in a finite market model is obtained by super-hedging a contingent claim connected with a martingale measure which is a solution of an auxiliary maximization problem.

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