Stochastic dominance conditions are given for n-variate utilityfunctions, when k-variate risk aversion is assumed for k = 1, 2, …, n. These conditions are expressed through a comparison of distribution functions, as...
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Stochastic dominance conditions are given for n-variate utilityfunctions, when k-variate risk aversion is assumed for k = 1, 2, …, n. These conditions are expressed through a comparison of distribution functions, as in the well-known univariate case, and through a comparison of random variables defined on the same probability space.
In this work, we propose deep learning-based algorithms for the computation of systemic shortfall risk measures defined via multivariate utility functions. We discuss the key related theoretical aspects, with a partic...
详细信息
In this work, we propose deep learning-based algorithms for the computation of systemic shortfall risk measures defined via multivariate utility functions. We discuss the key related theoretical aspects, with a particular focus on the fairness properties of primal optima and associated risk allocations. The algorithms we provide allow for learning primal optimizers, optima for the dual representation and corresponding fair risk allocations. We test our algorithms by comparison to a benchmark model, based on a paired exponential utility function, for which we can provide explicit formulas. We also show evidence of convergence in a case in which explicit formulas are not available.
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