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A numerical scheme for the quantile hedging problem. (English) Zbl 1459.91217

The research in this article is related to the important problems: numerical representation for the quantile hedging of options and stochastic target problems with controlled loss.
The authors study the numerical approximations to the quantile hedging price of a European claim in a nonlinear market with Markovian dynamics. More precisely, an equivalent stochastic target problem with the conditional probability of success as a new state variable in addition to the asset value process is considered.
The authors conduct an important convergence analysis in the monotone case combining backward stochastic differential equation arguments with the Barles and Jakobsen and Barles and Souganidis approaches for nonlinear PDEs. Numerical results for a specific application are given in Section 3. Basic guidelines for future research are also outlined.

MSC:

91G60 Numerical methods (including Monte Carlo methods)
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
91G20 Derivative securities (option pricing, hedging, etc.)

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