Conditional Risk Mappings

We introduce an axiomatic definition of a conditional convex risk mapping. By employing the techniques of conjugate duality we derive properties of conditional risk mappings. In particular, we prove a representation theorem for conditional risk mappings in terms of conditional expectations. We also develop dynamic programming relations for multistage optimization problems involving conditional risk mappings.Risk, Convex Analysis, Conjugate Duality, Stochastic Optimization, Dynamic Programming, Multi-Stage Programming

Asset liability management modeling using multi-stage mixed-integer stochastic programming

A pension fund has to match the portfolio of long-term liabilities with the portfolio of assets. Key instruments in strategic Asset Liability Management (ALM) are the adjustments of the contribution rate of the sponsor and the reallocation of the investments in several asset classes at various points of time. We formulate a multistage mixed-integer stochastic program to model this ALM process. Special attention is paid to the use of binary variables.

Stochastic multi-period multi-product multi-objective Aggregate Production Planning model in multi-echelon supply chain

In this paper a multi-period multi-product multi-objective aggregate production planning (APP) model is proposed for an uncertain multi-echelon supply chain considering financial risk, customer satisfaction, and human resource training. Three conflictive objective functions and several sets of real constraints are considered concurrently in the proposed APP model. Some parameters of the proposed model are assumed to be uncertain and handled through a two-stage stochastic programming (TSSP) approach. The proposed TSSP is solved using three multi-objective solution procedures, i.e., the goal attainment technique, the modified ε-constraint method, and STEM method. The whole procedure is applied in an automotive resin and oil supply chain as a real case study wherein the efficacy and applicability of the proposed approaches are illustrated in comparison with existing experimental production planning method