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Optimality of the replicating strategy for American options

Marek Kociński — 1999

Applicationes Mathematicae

The aim of this paper is to study the problem of optimality of replicating strategies associated with pricing of American contingent claims in the Cox-Ross-Rubinstein model with proportional transaction costs. We show that a replication of the option is always possible. We give sufficient conditions for the existence of a replicating strategy which is optimal, and also show an example of an optimal replicating strategy that is not optimal in the global sense.

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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