Price systems for markets with transaction costs and control problems for some finance problems

Details Price systems for markets with transaction costs and control problems for some finance problems Price systems for markets with transaction costs and control problems for some finance problems

2007-02-27

arxiv.org/abs/math/0702828v1

IMS Lecture Notes Monograph Series 2006, Vol. 52, 257-271

Mathematics

Probability

Published at http://dx.doi.org/10.1214/074921706000001094 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/p

Scientific paper

10.1214/074921706000001094

In a market with transaction costs, the price of a derivative can be expressed in terms of (preconsistent) price systems (after Kusuoka (1995)). In this paper, we consider a market with binomial model for stock price and discuss how to generate the price systems. From this, the price formula of a derivative can be reformulated as a stochastic control problem. Then the dynamic programming approach can be used to calculate the price. We also discuss optimization of expected utility using price systems.

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