在部分信息且市场利率非零的情形下,应用α-极大极小期望效用(α—MEU)模型区别投资者的含糊和含糊态度,研究资产预期收益率发生紊乱fdisorderl时的投资组合问题.首先,利用倒向随机微分方程理论刻画了α—MEU.其次,给出紊乱时刻的后验概率过程满足的随机微分方程(SDE),以及价值过程所满足的倒向随机微分方程(BSDE).最后,应用鞅论解出指数效用时的最优交易策略和价值过程的明确表达式.关键词:含糊和含糊态度:紊乱问题;鞅;交易策略;部分信息
A model of the α-maxmin expected utility(α-MEU) can be utilized to differentiate ambiguity and ambiguity attitude of an investor and to study the problem of investment portfolio, when the asset return has been disordered and the financial market has non-zero interest rate under partial information. First, the backward stochastic differential equation is used to characterize α-MEU. Secondly, it is proved that the posterior probability process of disorder moment satisfies a stochastic differential equation(SDE), and that the value process is the unique solution of a backward stochastic differential equation. Finally, by the techniques to the martingale, the explicit expressions of optimal trading strategy as well as of value process in the particular case of exponential utility are worked out.