带交易费用的指数效用无差别定价和套期保值策略

Exponential Utility of Indifference Prices and Hedging Strategy with Transaction Costs

本文研究了离散的带有交易费用的不完全市场的无差别定价和套期保值策略.通过引入一个新的概率测度,可以得到单阶段模型中的无差别价格及其相应的套期保值策略.利用一个非线性的迭代函数构造了多阶段市场的指数效用无差别定价,并得到了相应的定价测度和套期保值策略.可以证明此定价测度只有在交易费用均为零的情况下是鞅测度.

This article studies the indifference prices and hedging strategies in the presence of proportional transaction costs in the incomplete markets. By introducing a new probabilistic measure, the indifference price and the corresponding hedging strategy can be got in one period model. A probabilistic iterative algorithm is constructed for indifference prices of claims in a multiperiod incomplete model. And the corresponding pricing measure and the hedging strategy can be got. Pricing measure proves a martingale measure if the transaction cost is zero.