Multi-Objective Stochastic Optimization Programs for a Non-Life Insurance Company under Solvency Constraints

Kaucic, Massimiliano; Daris, Roberto

doi:10.3390/risks3030390

Cited by 7 publications

(6 citation statements)

References 51 publications

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“…Since the strict complementarity condition is satisfied at (ȳ,d), gphN K is normally regular at (r(ȳ),d). Combining (17) and (18), we conclude that the equality (17) holds. Hence,…”

Section: 2mentioning

confidence: 79%

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Asymptotic convergence of stationary points of stochastic multiobjective programs with parametric variational inequality constraint via SAA approach

Pang¹,

Meng²,

Wang³

2019

Journal of Industrial &Amp; Management Optimization

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We consider the sample average approximation method for a stochastic multiobjective programming problem constrained by parametric variational inequalities. The first order necessary conditions for the original problem and its sample average approximation (SAA) problem are established under constraint qualifications. By graphical convergence of set-valued mappings, the stationary points of the SAA problem converge to the stationary points of the true problem when the sample size tends to infinity. Under proper assumptions, the convergence of optimal solutions of SAA problems is also obtained. The numerical experiments on stochastic multiobjective optimization problems with variational inequalities are given to illustrate the efficiency of SAA estimators.

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“…Since the strict complementarity condition is satisfied at (ȳ,d), gphN K is normally regular at (r(ȳ),d). Combining (17) and (18), we conclude that the equality (17) holds. Hence,…”

Section: 2mentioning

confidence: 79%

“…This is a typical practical example. Other familiar practical examples are given in [2], [3], [4], [12], [18], [30] etc. In recent years stochastic multiobjective programs with equilibrium constraints play a nonnegligible role in mathematical programmings.…”

mentioning

confidence: 99%

Asymptotic convergence of stationary points of stochastic multiobjective programs with parametric variational inequality constraint via SAA approach

Pang¹,

Meng²,

Wang³

2019

Journal of Industrial &Amp; Management Optimization

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“…Median model [12] refers to in the condition of a set of demand with given number and location and a candidate facility location set, find the appropriate location for p facilities and assign each demand point to a specific facility, in order to achieve the lowest transportation cost between the factory and the demand point. The object function is given by (10) Constraints are given by (11) where N denotes the ... n costumer (demand point) in the research object, M denotes ... m candidate point in the research object, d l denotes the demand of the l-th point, c lj denotes unit transportation cost from location l to j , p is the number of facility points allowed to be built, A(j ) is the set of demand points covered by the facility point j , and B(l) is the set of facility point j covering the demand point l.…”

Section: ) Maximum Covering Modelmentioning

confidence: 99%

Clustering Control of Multi-Objective Problems with Application to E-commerce

Liang

Wang

Shi

2018

IJRC

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In the existing logistics distribution methods, the demand of customers is not considered. The goal of these methods is to maximize the vehicle capacity, which leads to the total distance of vehicles to be too long, the need for large numbers of vehicles and high transportation costs. To address these problems, a method of multi-objective clustering of logistics distribution route based on hybrid ant colony algorithm is proposed in this paper. Before choosing the distribution route, the customers are assigned to the unknown types according to a lot of customers attributes so as to reduce the scale of the solution. The discrete point location model is applied to logistics distribution area to reduce the cost of transportation. A mathematical model of multi-objective logistics distribution routing problem is built with consideration of constraints of the capacity, transportation distance, and time window, and a hybrid ant colony algorithm is used to solve the problem. Experimental results show that, the optimized route is more desirable, which can save the cost of transportation, reduce the time loss in the process of circulation, and effectively improve the quality of logistics distribution service.

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“…All the three problems include a portfolio performance constraint defined as a lower bound on the expected return on capital (ROC). Kaucic & Daris (2015) proposed an alternative approach to deal with multi-objective portfolio optimization problems with chance constraints and applied this optimization framework to an EU-based non-life insurance company that tries to minimize the risk of the discrepancy between assets and liabilities. The authors adopt shareholders' capital and investment weights as decision variables.…”

Section: Introductionmentioning

confidence: 99%

Minimum capital requirement and portfolio allocation for non-life insurance: a semiparametric model with Conditional Value-at-Risk (CVaR) constraint

Staino

Russo

Costabile

et al. 2022

Preprint

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We present an optimization problem to determine the minimum capital requirement for a non-life insurance company. The optimization problem imposes a non-positive Conditional Value-at-Risk (CVaR) of the insurer's net loss and a portfolio performance constraint. When expressing the optimization problem in a semiparametric form, we demonstrate its convexity for any integrable random variable representing the insurer's liability. Furthermore, we prove that the function defining the CVaR constraint in the semiparametric formulation is continuously differentiable when the insurer's liability has a continuous distribution. We use the Kelly-Cheney-Goldstein algorithm to solve the optimization problem in the semiparametric form and show its convergence. An empirical analysis is carried out by assuming three different liability distributions: a lognormal distribution, a gamma distribution, and a mixture of Erlang distributions with a common scale parameter. The numerical experiments show that the choice of the liability distribution plays a crucial role since marked differences emerge when comparing the mixture distribution with the other two distributions. In particular, the mixture distribution describes better the right tail of the empirical distribution of liabilities with respect to the other two distributions and implies higher capital requirements and different assets in the optimal portfolios.

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Multi-Objective Stochastic Optimization Programs for a Non-Life Insurance Company under Solvency Constraints

Cited by 7 publications

References 51 publications

Asymptotic convergence of stationary points of stochastic multiobjective programs with parametric variational inequality constraint via SAA approach

Asymptotic convergence of stationary points of stochastic multiobjective programs with parametric variational inequality constraint via SAA approach

Clustering Control of Multi-Objective Problems with Application to E-commerce

Minimum capital requirement and portfolio allocation for non-life insurance: a semiparametric model with Conditional Value-at-Risk (CVaR) constraint

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