I will present some current problems in the context of option pricing and quantitative risk measurement.
Within the option pricing context, robust, fast and accurate numerical methods are appealing to efficiently calibrate the pricing models with market data.
In the context of risk management, a classical but still important problem is the estimation of the loss distribution of a portfolio over a specified time horizon and the associated risk measures. The risk is typically measured by means of the well-known Value-at-Risk (VaR), although regulatory changes are pushing financial companies to move from the VaR to the Expected Shortfall computation.

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