A Martingale approach to optimal portfolios with jump-diffusions and benchmarks
Michelbrink, Daniel (2012) A Martingale approach to optimal portfolios with jump-diffusions and benchmarks. PhD thesis, University of Nottingham.
We consider various portfolio optimization problems when the stock prices follow jump-diusion processes. In the first part the classical optimal consumption-investment problem is considered. The investor's goal is to maximize utility from consumption and terminal wealth over a finite investment horizon. We present results that modify and extend the duality approach that can be found in Kramkov and Schachermayer (1999). The central result is that the optimal trading strategy and optimal equivalent martingale measure can be determined as a solution to a system of non-linear equations.
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