We consider a controlled diffusion process [Inline formula] where the controller is allowed to choose drift [Inline formula] and volatility [Inline formula] from a set [Inline formula] when [Inline formula]. By choosing the largest [Inline formula] at every point in time, an extremal
process is constructed which is under suitable time changes stochastically larger than any other admissible process. This observation immediately leads to a very simple solution of problems where ruin or hitting probabilities have to be minimized. Under further conditions this extremal process
also minimizes ‘drawdown’ probabilities.
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time changed continuous Martingale
Document Type: Research Article
Department of Mathematics, Karlsruhe Institute of Technology, D-76128,Karlsruhe, Germany
Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, MI,48109, USA
Publication date: March 4, 2014