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Stability, empirical estimates and scenario generation in stochastic optimization - applications in finance
Kybernetika, Tome 53 (2017) no. 6, pp. 1026-1046
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Economic and financial processes are mostly simultaneously influenced by a random factor and a decision parameter. While the random factor can be hardly influenced, the decision parameter can be usually determined by a deterministic optimization problem depending on a corresponding probability measure. However, in applications the "underlying" probability measure is often a little different, replaced by empirical one determined on the base of data or even (for numerical reason) replaced by simpler (mostly discrete) one. Consequently, real one and approximate one correspond to applications. In the paper we try to investigate their relationship. To this end we employ the results on stability based on the Wasserstein metric and ${\cal L}_{1}$ norm, their applications to empirical estimates and scenario generation. Moreover, we apply the achieved new results to simple financial applications. The corresponding model will a problem of stochastic programming.
Economic and financial processes are mostly simultaneously influenced by a random factor and a decision parameter. While the random factor can be hardly influenced, the decision parameter can be usually determined by a deterministic optimization problem depending on a corresponding probability measure. However, in applications the "underlying" probability measure is often a little different, replaced by empirical one determined on the base of data or even (for numerical reason) replaced by simpler (mostly discrete) one. Consequently, real one and approximate one correspond to applications. In the paper we try to investigate their relationship. To this end we employ the results on stability based on the Wasserstein metric and ${\cal L}_{1}$ norm, their applications to empirical estimates and scenario generation. Moreover, we apply the achieved new results to simple financial applications. The corresponding model will a problem of stochastic programming.
DOI : 10.14736/kyb-2017-6-1026
Classification : 90C15
Keywords: stochastic programming problems; probability constraints; stochastic dominance; stability; Wasserstein metric; ${\cal L}_{1}$ norm; Lipschitz property; empirical estimates; scenario; error approximation; financial applications; loan; debtor; installments; mortgage; bank 
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Kaňková, Vlasta. Stability, empirical estimates and scenario generation in stochastic optimization - applications in finance. Kybernetika, Tome 53 (2017) no. 6, pp. 1026-1046. doi: 10.14736/kyb-2017-6-1026

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