Parameter continuity of the ergodic cost for a growth optimal portfolio with proportional transaction costs

Some results are given for a continuous time long run growth optimal portfolio that has proportional costs consisting of the sum of a fixed proportional cost and a cost that is proportional to the volume of each transaction. An obligatory portfolio diversification is given that requires at least a small portion of the wealth be invested in each asset. It is assumed that the price of each asset is obtained from a Levy noise stochastic equation whose coefficients depend on an unknown parameter from a compact set. It is shown that the optimal cost is a continuous function of the unknown parameter.

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