Optimization with multivariate conditional value-at-risk constraints

For many decision making problems under uncertainty, it is crucial to develop risk-averse models and specify the decision makers' risk preferences based on multiple stochastic performance measures (or criteria). Incorporating such multivariate preference rules into optimization models is a fairly recent research area. Existing studies focus on extending univariate stochastic dominance rules to the multivariate case. However, enforcing multivariate stochastic dominance constraints can often be overly conservative in practice. As an alternative, we focus on the widely-applied risk measure conditional value-at-risk (CVaR), introduce a multivariate CVaR relation, and develop a novel optimization model with multivariate CVaR constraints based on polyhedral scalarization. To solve such problems for finite probability spaces we develop a cut generation algorithm, where each cut is obtained by solving a mixed integer problem. We show that a multivariate CVaR constraint reduces to finitely many univariate CVaR constraints, which proves the finite convergence of our algorithm. We also show that our results can be naturally extended to a wider class of coherent risk measures. The proposed approach provides a flexible, and computationally tractable way of modeling preferences in stochastic multi-criteria decision making. We conduct a computational study for a budget allocation problem to illustrate the effect of enforcing multivariate CVaR constraints and demonstrate the computational performance of the proposed solution methods

Project portfolio management: capacity allocation, downsizing decisions and sequencing rules.

This paper aims to gain insight into capacity allocation, downsizing decisions and sequencing rules when managing a portfolio of projects. By downsizing, we mean reducing the scale or size of a project and thereby changing the project's content. In previous work, we have determined the amount of critical capacity that is optimally allocated to concurrently executed projects with deterministic or stochastic workloads when the impact of downsizing is known. In this paper, we extend this view with the possibility of sequential processing, which implies that a complete order is imposed on the projects. When projects are sequenced instead of executed in parallel, two effects come into play: firstly, unused capacity can be shifted to later projects in the same period; and secondly, reinvestment revenues gain importance because of the differences in realization time of the sequenced projects. When project workloads are known, only the second effect counts; when project workloads are stochastic, however, the project's capacity usage is uncertain so that unused capacity can be shifted to later projects in the same period. In this case, both effects need to be taken into account. In this paper, we determine optimal sequencing rules when the selection and capacity-allocation decisions for a set of projects have already been made. We also consider a combination of parallel and sequential planning and we perform simulation experiments that confirm the appropriateness of our capacity-allocation methods.Project portfolio management; Downsizing; Sequencing;

Conservation Payments under Risk: A Stochastic Dominance Approach

Conservation payments can be used to preserve forest and agroforest systems in developing countries. To explain landowners’ land-use decisions and determine the appropriate conservation payments, it is necessary to focus on risk associated with agricultural price and yield volatility. A theoretical framework is provided for assessing land-use allocation problems under risk and setting risk-efficient conservation payments when returns are not necessary normally distributed. Stochastic dominance rules are used to derive conditions for determining the conservation payments required to guarantee that the environmentally-preferred land use dominates, even when land uses are not considered to be mutually exclusive. An empirical application to shaded-coffee protection in the biologically important El Chocó region of West Ecuador shows that conservation payments required for preserving shaded-coffee areas are much higher than those calculated under the assumption of risk-neutrality. Further, the extant distribution of land has a strong impact on the required conservation payments.risk, conservation payments, land allocation, stochastic dominance, agroforest systems, portfolio diversification

Optimization with multivariate conditional value-at-risk constraints

For many decision making problems under uncertainty, it is crucial to develop risk-averse models and specify the decision makers' risk preferences based on multiple stochastic performance measures (or criteria). Incorporating such multivariate preference rules into optimization models is a fairly recent research area. Existing studies focus on extending univariate stochastic dominance rules to the multivariate case. However, enforcing multivariate stochastic dominance constraints can often be overly conservative in practice. As an alternative, we focus on the widely-applied risk measure conditional value-at-risk (CVaR), introduce a multivariate CVaR relation, and develop a novel optimization model with multivariate CVaR constraints based on polyhedral scalarization. To solve such problems for finite probability spaces we develop a cut generation algorithm, where each cut is obtained by solving a mixed integer problem. We show that a multivariate CVaR constraint reduces to finitely many univariate CVaR constraints, which proves the finite convergence of our algorithm. We also show that our results can be naturally extended to a wider class of coherent risk measures. The proposed approach provides a flexible, and computationally tractable way of modeling preferences in stochastic multi-criteria decision making. We conduct a computational study for a budget allocation problem to illustrate the effect of enforcing multivariate CVaR constraints and demonstrate the computational performance of the proposed solution methods

Conservation Payments under Risk: A Stochastic Dominance Approach

Conservation payments can be used to preserve forest and agroforest systems. To explain landowners’ land-use decisions and determine appropriate conservation payments, it is necessary to focus on revenue risk. Marginal conditional stochastic dominance rules are used to derive conditions for determining the conservation payments required to guarantee that the environmentally-preferred land use dominates. An empirical application to shaded-coffee protection in the biologically important Chocó region of West-Ecuador shows that conservation payments required for preserving shaded-coffee areas are much higher than those calculated under risk-neutral assumptions. Further, the extant distribution of land has strong impacts on the required payments.agroforest systems, conservation payments, land allocation, portfolio diversification, risk, stochastic dominance

Budgetary policies and available actions: a generalisation of decision rules for allocation and research decisions

The allocation problem in health care can be characterised as a mathematical programming problem but attempts to incorporate uncertainty in costs and effect have suffered from important limitations. A two stage stochastic mathematical programming formulation is developed and applied to a numerical example to explore and demonstrate the implications of this more general and comprehensive approach. The solution to the allocation problem for different budgets, budgetary policies, and available actions are then demonstrated. This analysis is used to evaluate different budgetary policies and examine the adequacy of standard decision rules in cost-effectiveness analysis. The research decision is then considered alongside the allocation problem. This more general formulation demonstrates that the value of further research depends on: i) the budgetary policy in place; ii) the realisations revealed during the budget period; iii) remedial actions that may be available; and iv) variability in parameters values.

Obligation Rules for Minimum Cost Spanning Tree Situations and their Monotonicity Properties

We introduce the class of Obligation rules for minimum cost spanning tree situations.The main result of this paper is that such rules are cost monotonic and induce also population monotonic allocation schemes.Another characteristic of Obligation rules is that they assign to a minimum cost spanning tree situation a vector of cost contributions which can be obtained as product of a double stochastic matrix with the cost vector of edges in the optimal tree provided by the Kruskal algorithm.It turns out that the Potters value (P-value) is an element of this class.

Allocation of risk capital based on iso-entropic coherent risk measure

Journal of Industrial Engineering and Management OmniaScience User Username Password Remember me Scholar Sponsorship - UPC BarcelonaTech - Beijing Jiaotong University - UPV - UPCT Article Tools Indexing metadata Supplementary files Finding References Review policy Email this article (Login required) Email the author (Login required) Printed Edition News Indexing SJR (Scopus) SCImago Journal & Country Rank See more: DOAJ, InRecs... Journal Content Search Browse By Issue By Author By Title Information For Readers For Authors For Librarians Visitors Locations of visitors to this page Home About Log In Archives Submissions Publication fee Indexing & Statistics Home > Vol 8, No 2 (2015) > Zheng Allocation of risk capital based on iso-entropic coherent risk measure Chengli Zheng, Yan Chen Abstract Purpose: The potential of diversified portfolio leads to the risk capital allocation problem. There are many kinds of methods or rules to allocate risk capital. However, they have flaws, such as non-continuity, unfairness. In order to get a better method, we propose a new risk measure to be the base of risk capital allocation rule. Design/methodology/approach: We proposed two kinds of allocation methods: one is marginal risk contribution based on iso-entropic coherent risk measure(IE), the other one is to combine the minimal excess allocation(EBA) principle and IE into risk capital allocation. The iso-entropic coherent risk measure has many advantages over others; it is continuous and more powerful in distinguishing risks, consistent with higher-order stochastic dominances than other risk measures. And EBA is consistent with the amount of risk, which means fairness for risk capital allocation. Findings: Through cases, simulations and empirical application, it shows that these two allocation rules satisfy some good properties, can be more efficient, more precise and fairer. And the EBA based on IE may be the better one. Research limitations/implications: However, there are some problems still open. One is how to treat the negative value of allocation. Second is that the consistence between the allocated risk capital and the amount of the risk needs to be studied further. Originality/value: A good risk measure is very important for risk capital allocation. We proposed two methods to deal with risk capital allocation based on a new coherent risk measure called iso-entropic risk measure, which is smooth and consistent with higher-order stochastic dominance and has higher resolution of risk. It shows that the risk capital allocation rules based on iso-entropic risk measure are better than the other rules.Peer Reviewe

Mortality Contingent Claims: Impact of Capital Market, Income, and Interest Rate Risk

In this paper, we consider optimal insurance, portfolio allocation, and consumption rules for a stochastic wage earner with CRRA preferences whose lifetime is random. In a continuous time framework, the investor has to decide among short and long positions in mortality contingent claims a.k.a. life insurance, stocks, bonds, and money market investment when facing a risky stock market and interest rate risk. We find an analytical solution for the complete market case in which human capital is exactly priced. We also extend the analysis to the case where income is unspanned. An illustrative analysis shows when the wage earner’s demand for life insurance switches to the demand for annuities.