Dynamic Asset Allocation with Uncertain Jump Risks: A Pathwise Optimization Approach

This paper studies the dynamic portfolio choice problem with ambiguous jump risks in a multidimensional jump-diffusion framework. We formulate a continuous-time model of incomplete market with uncertain jumps. We develop an efficient pathwise optimization procedure based on the martingale methods and minimax results to obtain closed-form solutions for the indirect utility function and the probability of the worst scenario. We then introduce an orthogonal decomposition method for the multidimensional problem to derive the optimal portfolio strategy explicitly under ambiguity aversion to jump risks. Finally, we calibrate our model to real market data drawn from 10 international indices and illustrate our results by numerical examples. The certainty equivalent losses affirm the importance of jump uncertainty in optimal portfolio choice.