An example of indifference prices under exponential preferences
The purpose of this paper is to provide new insights and ideas for pricing and hedging in incomplete markets. Incompleteness is generated by non-traded assets and the underlying problem is how to price and hedge derivatives that are written on such securities. The level of the non-traded assets can be fully observed across time, but it is not feasible to create a perfect replicating portfolio. Therefore, the market is incomplete and alternatives to the arbitrage pricing must be developed in order to specify the appropriate price concept and to define the related risk management. The paper is designed to expose some fundamental ingredients and intuitive elements of the indifference valuation theory. The authors consider a market environment with log-normal dynamics of the stock and general diffusion dynamics for the correlated non-traded asset. They establish that the indifference price of the European claim, written exclusively on the related non-traded asset, is given as a nonlinear functional of the payoff represented solely in terms of the risk aversion, the correlation and the pricing measure. The pricing measure is independent of the risk preferences and, among all martingale measures, it has the minimal entropy with respect to the historical measure.
scientific article; zbMATH DE number 2118697