Optimal Investment Strategy Under Partial Information In Market With Transaction Costs

This paper attacks a problem of maximizing the expected utility from terminalwealth with proportional transaction costs under the case of partial information.The optimal estimate for the average appreciation rate of the risky asset is acquiredby means of Kalman filter in the case of partial information with normal distri-bution. By means of singular stochastic control, the paper provides an optimalstrategy which satisfies PDE with free boundaries. The PDE is solved by a dis-crete stochastic dynamic programming based on a Markov chain approximation.Provided that the utility function is CARA the paper establishes an algorithm.Several essential parameters which have prominent e?ects on the algorithm havebeen discussed. Another numerical scheme, finite di?erence, which is also suit-able to the market model with transaction costs, is compared with the Markovchain approximation. After that, some e?cient Monte Carlo techniques are intro-duced. Furthermore, making use of Monte Carlo technique, partial information iscompared with complete information by analyzing the value of information andcertainty equivalent. The impact of transaction costs can be observed by no trans-action costs equivalent. An example and comparative statics are shown and theproperties of partial information have been obtained. In the end, the model abovehas been extended to optimal investment-consumption problem and another partialinformation model, Bernoulli beliefs. The algorithm solving optimal investment-consumption problem and the filter result based on the partial information modelhave been obtained.