  We study the problem of option pricing and hedging strategies within the
frame-work of risk-return arguments. An economic agent is described by a
utility function that depends on profit (an expected value) and risk (a
variance). In the ideal case without transaction costs the optimal strategy for
any given agent is found as the explicit solution of a constrained optimization
problem. Transaction costs are taken into account on a perturbative way. A
rational option price, in a world with only these agents, is then determined by
considering the points of view of the buyer and the writer of the option. Price
and strategy are determined to first order in the transaction costs.
