# Optimal strategies with option compensation under mean reverting returns or volatilities

## Abstract

We study the problem of a fund manager whose contractual incentive is given by the sum of a constant and a variable term. The manager has a power utility function and the continuous time stochastic processes driving the dynamics of the market prices exhibit mean reversion either in the volatilities or in the expected returns. We provide an approximation for the optimal wealth and for the optimal strategy based on affine processes and the fast Fourier transform.

## Keywords

Investment analysis Portfolio management Convex incentives Optimal control Fourier transform Mean reverting processes## References

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