Ключевые слова и фразы:хеджирование, экспоненциальная функ ция полезности, неприятие риска, опциональное разложение.1. Introduction. In this paper we consider a financial market with an agent who has to satisfy a contingent claim, e.g., an option, at final time T. The agent, who has the possibility of investing in an asset of the underlying financial market, has to decide on a trading strategy and there are, at least, two natural, but different possibilities: utility maximization and superhedging. We will investigate the relationship between these two concepts and show how superhedging can be interpreted as the limit of utility maximiza tion. This interpretation will give some new insight into the notion of superhedging.For example the notion of superhedging in general does not yield a unique outcome, i.e., there are different superhedging strategies that lead to different terminal wealth at time T. But by looking at superhedging as a limit of utility maximization one is naturally led to a special, unique outcome.Let us assume we are given a finite probability space Q = {tt>i,... ,u>jv}, a finite time horizon T G N, a filtration (.^t)t=o,i,...,r, and a probability measure P. For finite CI we always assume that P[CJ»] > 0 for all i = 1,..., N. Furthermore we assume, as is typically done in arbitrage pricing theory, that &o is trivial. The market consists of a stock S = (St)t=o,i,...,T, i-e., an R-valued adapted process, and a riskless bond B. We assume without loss of generality that the stock S represents the discounted price process, i.e., that it is denoted in terms of units of the riskless bond, and that the bond is constant equal to 1.The stock process S can be represented by an event tree. Each node in the tree corresponds to an atom'F €«ft,t = 0,l,...,T. By an atom F G &t we mean an element F G & u
