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Exponential utility maximization under partial information

机译:部分信息下的指数效用最大化

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We consider the exponential utility maximization problem under partial information. The underlying asset price process follows a continuous semimartingale and strategies have to be constructed when only part of the information in the market is available. We show that this problem is equivalent to a new exponential optimization problem which is formulated in terms of observable processes. We prove that the value process of the reduced problem is the unique solution of a backward stochastic differential equation (BSDE) which characterizes the optimal strategy. We examine two particular cases of diffusion market models for which an explicit solution has been provided. Finally, we study the issue of sufficiency of partial information.
机译:我们考虑了部分信息下的指数效用最大化问题。潜在的资产价格过程遵循一个连续的半市场,当市场中只有部分信息可用时,必须构造策略。我们表明,该问题等效于根据可观察过程提出的新的指数优化问题。我们证明了减少问题的价值过程是表征最优策略的后向随机微分方程(BSDE)的唯一解。我们研究了扩散市场模型的两种特殊情况,并为其提供了明确的解决方案。最后,我们研究了部分信息的充分性问题。

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