Jump-Diffusion Risk-Sensitive Benchmarked Asset Management

AbstractIn earlier works (Davis and Lleo, 2011b; Davis and Lleo, 2012), we showed that jump-diffusion risk-sensitive asset management problem without benchmark admit a unique classical (C1, 2) solution. In this article we extend these solution techniques to a benchmarked asset management problem with jumps. Benchmarked asset management problems are highly relevant to the financial industry: most investment funds have a benchmark, such as a financial index or a customized portfolio, against which their performance is assessed. We show here under two different sets of assumptions that the stochastic control problem associated with the benchmarked aset management problem admits a unique C1, 2 solution and that the optimal investment strategy exists and is unique.

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