Risk-Sensitive Investment in a Market with Animal Spirits

A new jump diffusion regime-switching model is introduced, which allows for linking jumps in asset prices with regime changes. We prove the existence and uniqueness of the solution to the risk-sensitive asset management criterion maximisation problem in this setting. We provide an ODE for the optimal value function, which may be efficiently solved numerically. Relevant probability measure changes are discussed in the appendix. The approach of Klebaner & Lipster (2014) is used to prove the martingale property of the relevant density processes.

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