Or simply: why do we call equivalent martingale measures as risk-neutral measures?
In the utility or game theory, when we consider a person's preferences to certain outcomes, we often deal with the utility functions. For example, if we consider an investor with a utility function U whose return on a portfolio Π is xΠ, we assume that he choose a portfolio that maximizes his expected utility Π∗ such that EU(xΠ∗)=supΠEU(xΠ).
The risk-neutral valuation - taking expectations w.r.t. martingale measures equivalent to the real-world ones - is used in quant finance a lot for the pricing purposes. I do understand the theory behind this method, and the relation with non-arbitrage arguments. I wonder though, whether there is any relation with the risk-neutrality as in the paragraph above.
I thought of the following idea: let us think of a fair price for a contract (when we write it) as the highest one at which the agent will buy it. The agent A with utility UA and expectation of prices EA has to make a choice between the zero utility (when he does not buy contract) and EAUA(e−rTCT−C0)
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