A Dynamic Investment Model with Control on the Portfolio's Worst Case Outcome

This paper considers a portfolio problem with control on downside losses. Incorporating the worst-case portfolio outcome in the objective function, the optimal policy is equivalent to the hedging portfolio of a European option on a dynamic mutual fund that can be replicated by market primary assets. Applying the Black-Scholes formula, a closed-form solution is obtained when the utility function is HARA and asset prices follow a multivariate geometric Brownian motion. The analysis provides a useful method of converting an investment problem to an option pricing model.

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