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arXiv · 1210.3800

A Note on Applications of Stochastic Ordering to Control Problems in Insurance and Finance

Nicole Bauerle·Erhan Bayraktar
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Abstract

We consider a controlled diffusion process $(X_t)_{t\ge 0}$ where the controller is allowed to choose the drift $μ_t$ and the volatility $σ_t$ from a set $\K(x) \subset \R\times (0,\infty)$ when $X_t=x$. By choosing the largest $\fracμ{σ^2}$ 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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Nicole Bauerle, Erhan Bayraktar. 2013-07-14. A Note on Applications of Stochastic Ordering to Control Problems in Insurance and Finance. https://doi.org/10.1080/17442508.2013.778861

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