We prove a strong duality result for a linear programming problem which has the interpretation of being a discretised optimal Skorokhod embedding problem, and we recover this continuous time problem as a limit of the discrete problems. With the discrete setup we show that for a suitably chosen objective function, the optimiser takes the form of a hitting time for a random walk. In the limiting problem we then reprove the existence of the Root, Rost, and cave embedding solutions of the Skorokhod embedding problem.The main strength of this approach is that we can derive properties of the discrete problem more easily than in continuous time, and then prove that these properties hold in the limit. For example, the strong duality result gives dual optimisers, and our limiting arguments can be used to derive properties of the continuous time dual functions, known to represent a superhedging portfolio.

A leveraged exchange traded fund (LETF) is an exchange traded fund that uses financial derivatives to amplify the price changes of a basket of goods. In this paper, we consider the robust hedging of European options on a LETF, finding model-free bounds on the price of these options.To obtain an upper bound, we establish a new optimal solution to the Skorokhod embedding problem (SEP) using methods introduced in Beiglböck-Cox-Huesmann. This stopping time can be represented as the hitting time of some region by a Brownian motion, but unlike other solutions of e.g. Root, this region is not unique. Much of this paper is dedicated to characterising the choice of the embedding region that gives the required optimality property. Notably, this appears to be the first solution to the SEP where the solution is not uniquely characterised by its geometric structure, and an additional condition is needed on the stopping region to guarantee that it is the optimiser. An important part of determining the optimal region is identifying the correct form of the dual solution, which has a financial interpretation as a model-independent superhedging strategy.

Determining accurate capital requirements is a central activity across the life insurance industry. This is computationally challenging and often involves the acceptance of proxy errors that directly impact capital requirements. Within simulation-based capital models, where proxies are being used, capital estimates are approximations that contain both statistical and proxy errors. Here, we show how basic error analysis combined with targeted exact computation can entirely eliminate proxy errors from the capital estimate. Consideration of the possible ordering of losses, combined with knowledge of their error bounds, identifies an important subset of scenarios. When these scenarios are calculated exactly, the resulting capital estimate can be made devoid of proxy errors. Advances in the handling of proxy errors improve the accuracy of capital requirements.

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