VALUATION OF CLAIMS ON NONTRADED ASSETS USING UTILITY MAXIMIZATION
研究如何利用类似的可交易资产或指数对非交易资产索取权进行定价和对冲，通过引入第二个非交易对数布朗运动资产到Merton投资模型中，采用效用最大化和对偶方法得到最优对冲和保留价格的近似解。
A topical problem is how to price and hedge claims on nontraded assets. A natural approach is to use for hedging purposes another similar asset or index which is traded. To model this situation, we introduce a second nontraded log Brownian asset into the well‐known Merton investment model with power law and exponential utilities. The investor has an option on units of the nontraded asset and the question is how to price and hedge this random payoff. The presence of the second Brownian motion means that we are in the situation of incomplete markets. Employing utility maximization and duality methods we obtain a series approximation to the optimal hedge and reservation price using the power utility. The problem is simpler for the exponential utility, and in this case we derive an explicit representation for the price. Price and hedging strategy are computed for some example options and the results for the utilities are compared.