Sample average approximation of multiobjective stochastic optimization problems with application in insurance
Abstract
The article describes a technique for solving multiobjective stochastic optimization problems. As a generalized model of a stochastic system to be optimized a vector (input-random output) system is used. Ran- dom outputs are converted into a vector of deterministic performance and risk indicators. The problem is to find those inputs that correspond to a Pareto-optimal values of output indicators. The problem is approximated by a sequence of deterministic multi-criteria optimization problems, where, for example, the objective vector function is a sample average approximation of the original one and the feasible set is a discrete sample approximation of the feasible inputs. Approximate optimal solutions are defined as weakly Pareto-efficient ones within some vector tolerance. Convergence analysis includes establishing convergence of the general approx- imation scheme and establishing conditions of convergence with probability one under proper regulation of sampling parameters. The proposed technique is illustrated on a computer system for supporting multi-criteria optimization of insurance business.
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BibTeX
@misc{norkin2026sample,
title = {{Sample average approximation of multiobjective stochastic optimization problems with application in insurance}},
author = {Bogdan Norkin},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18159},
eprint = {2609.18159},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18159},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Sample average approximation of multiobjective stochastic optimization problems with application in insurance
AU - Bogdan Norkin
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.18159
UR - https://arxiv.org/abs/2609.18159
AB - The article describes a technique for solving multiobjective stochastic optimization problems. As a generalized model of a stochastic system to be optimized a vector (input-random output) system is used. Ran- dom outputs are converted into a vector of deterministic performance and risk indicators. The problem is to find those inputs that correspond to a Pareto-optimal values of output indicators. The problem is approximated by a sequence of deterministic multi-criteria optimization problems, where, for example, the objective vector function is a sample average approximation of the original one and the feasible set is a discrete sample approximation of the feasible inputs. Approximate optimal solutions are defined as weakly Pareto-efficient ones within some vector tolerance. Convergence analysis includes establishing convergence of the general approx- imation scheme and establishing conditions of convergence with probability one under proper regulation of sampling parameters. The proposed technique is illustrated on a computer system for supporting multi-criteria optimization of insurance business.
ER -