Pathwise versions of the Burkholder-Davis-Gundy inequality. (English) Zbl 1352.60060
Motivated by hedging considerations from mathematical finance, the authors give a new proof of the Burkholder-Davis-Gundy (BDG) inequalities, which give a comparison between the running maximum of a martingale and its quadratic variation.
The inequalities are obtained as a consequence of deterministic inequalities which are then applied pathwise to the given martingale. Taking expectations in these inequalities then yields the BDG inequalities.
The inequalities are obtained as a consequence of deterministic inequalities which are then applied pathwise to the given martingale. Taking expectations in these inequalities then yields the BDG inequalities.
Reviewer: Fraser Daly (Edinburgh)
MSC:
| 60G42 | Martingales with discrete parameter |
| 60E15 | Inequalities; stochastic orderings |
| 60G46 | Martingales and classical analysis |
| 91G20 | Derivative securities (option pricing, hedging, etc.) |
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