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Risk estimates for dynamic hedging using convex probability bounds

In this paper, we employ convex optimization techniques to compute upper and lower bounds on the tail of an unknown probability distribution given its first m moments. We then apply this to dynamic hedging problems, where we estimate a specific quantile of the wealth balance (hedging error) distribution, known as its value-at-risk. A backward recursive algorithm on a multinomial lattice is used to compute the required moments of the wealth balance. Combining this with the convex optimization probability bounds results in an efficient methodology for estimating the risk resulting from a dynamic hedge.