Recovering the payoff structure of a utility maximizing agent

Any agent with access to information that is not available to the market at large is considered an ‘insider’. It is possible to interpret the effect of this private information as change in the insider’s probability measure. In the case of exponential utility, logarithm of the Radon-Nikodym derivative for the change in measure will appear as a random endowment in the objective the insider would maximize with respect to the original measure. The goal of this paper is to find conditions under which it is possible to recover the structure of this random endowment given only a single trajectory of his/her wealth. To do this, it is assumed that the random endowment is a function of the terminal value of the state variable and that the market is complete.