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A note on applications of stochastic ordering to control problems in insurance and finance

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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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Keywords: 60H30; 91B30; ruin problem; stochastic ordering; time changed continuous Martingale

Document Type: Research Article

Affiliations: 1: Department of Mathematics, Karlsruhe Institute of Technology, D-76128,Karlsruhe, Germany 2: Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, MI,48109, USA

Publication date: March 4, 2014

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