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A Dynamic Investment Model with Control on the Portfolio's Worst Case Outcome
Author(s) -
Zhao Yonggan,
Haussmann Ulrich,
Ziemba William T.
Publication year - 2003
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/1467-9965.t01-1-00177
Subject(s) - portfolio , downside risk , replicating portfolio , outcome (game theory) , economics , geometric brownian motion , black–litterman model , merton's portfolio problem , black–scholes model , investment (military) , econometrics , investment strategy , portfolio optimization , asset (computer security) , financial economics , microeconomics , computer science , volatility (finance) , economy , computer security , diffusion process , politics , political science , service (business) , profit (economics) , law
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.