A Framework Algorithm to Compute Optimal Asset Allocation for Retirement with Behavioral Utilities

The question of optimal strategic asset allocation for investors with behavioural utilities saving for retirement is addressed. To date this problem has been studied assuming that an investor is rational in the sense when making investment decisions the preference relation of the investor satisfies all the axioms of choice. Research in behavioural science indicates that investment related decisions of many people do not satisfy the axioms of choice. Our interest is in developing a platform that allows the use of a broader class of utilities that may or may not satisfy the axioms of choice. Such utilities may not be convex. Our interest is in developing a framework algorithm that enables a user considerable flexibility in how their needs may be specified. For illustrative purposes a binomial tree is used to model asset returns, although the method developed can be used with more elaborate models.Work supported by the National Science Foundation grant CCR-9988205 and Office of Naval Research grant N00014-96-1-0274.     

Integrating long-term care insurance purchase decisions with saving and investment for retirement

Risk related to long-term care (LTC) is high for the elderly. Planning for LTC is now regarded as the ‘third leg’ of retirement planning. In this paper, planning for LTC is integrated with saving and investment decisions for an integrated approach to retirement planning. Optimal LTC insurance purchase decisions are obtained by developing a trade-off between post-retirement LTC costs and LTC insurance premiums paid and coverage received. Integrating insurance purchase with wealth evolution, consisting of saving and investment decisions, allows addressing affordability issues.Two-way branching models are used for the stochastic health events and asset returns. The problem, formulated as a nonlinearly constrained mixed-integer optimization problem, is solved using a heuristic. Sensitivity analyses are performed for initial health and wealth status. Some important aspects of an individual’s behavioral preferences are also addressed in this framework to provide more robust decision support.     

Integrating long-term care insurance purchase decisions with saving and investment for retirement

Risk related to long-term care (LTC) is high for the elderly. Planning for LTC is now regarded as the ‘third leg’ of retirement planning. In this paper, planning for LTC is integrated with saving and investment decisions for an integrated approach to retirement planning. Optimal LTC insurance purchase decisions are obtained by developing a trade-off between post-retirement LTC costs and LTC insurance premiums paid and coverage received. Integrating insurance purchase with wealth evolution, consisting of saving and investment decisions, allows addressing affordability issues.Two-way branching models are used for the stochastic health events and asset returns. The problem, formulated as a nonlinearly constrained mixed-integer optimization problem, is solved using a heuristic. Sensitivity analyses are performed for initial health and wealth status. Some important aspects of an individual’s behavioral preferences are also addressed in this framework to provide more robust decision support.     

Portfolio selection for individual passive investing

This paper considers passive fund selection from an individual investor's perspective. The growth of the passive fund market over the past decade is staggering. Individual investors who wish to buy these funds for their retirement and brokerage accounts have many options and are faced with a difficult selection problem. Which funds do they invest in, and in what proportions? We develop a novel statistical methodology to address this problem by adapting recent advances in posterior summarization. A Bayesian decision‐theoretic approach is presented to construct optimal sparse portfolios for individual investors over time.     

Multicriteria decision aid in financial management

The financial decisions of an organization are usually included in the context of optimization. Concerning a long-term period, there are decisions related to the optimal allocation of funds, and decisions related to the optimal financial structure. In the short-term case, the decisions are related to the optimization of stocks, cash, accounts receivable, current liabilities, etc. The financial theory analyzes these decisions, mainly from an optimal point of view. The optimal character of such decisions has led researchers to propose operations research techniques to solve the problems that are inherent in such decisions. This paper examines the contribution of multicriteria analysis in solving financial decision problems in a realistic context. The paper also includes an extensive bibliography on the subject.     

Optimal retirement strategy with a negative wealth constraint

This paper investigates an optimal consumption, portfolio, and retirement time choice problem of an individual with a negative wealth constraint. We obtain analytical results of the optimal consumption, investment, and retirement behaviors and discuss the effect of the negative wealth constraint on the optimal behaviors. We find that, as an individual can borrow more with better credit, she is more likely to retire at a higher wealth level, to consume more, and to invest more in risky assets.     

Design of group decisions II. In spaces of partial order fuzzy relations

For the case of initial data in the problem of group choice represented as fuzzy partial orderings two problems are solved: (1) design of a set group decisions which satisfy the Pareto unanimity principlle and stay ‘halfway’ between initial relations and (2) design of a unique group decision.     

General methods of elliptic minimization

We provide general methods in the calculus of variations for the anisotropic Plateau problem in arbitrary dimension and codimension. Given a collection of competing “surfaces” that span a given “bounding set” in an ambient metric space, we produce one minimizing an elliptic area functional. The collection of competing surfaces is assumed to satisfy a set of geometrically-defined axioms. These axioms hold for collections defined using any combination of homological, cohomological or linking number spanning conditions. A variety of minimization problems can be solved, including sliding boundaries.     

Integrating optimal annuity planning with consumption-investment selections in retirement planning

Annuities can be effective tools in managing longevity risk in retirement planning. This paper develops a framework that merges annuity purchase decisions with consumption-investment selections in retirement planning. After introducing a pricing and a benefit payment model for an annuity, we construct a multi-period wealth evolution model. An optimization problem is formulated with an objective of maximizing lifetime utility of consumption and wealth. Optimal decisions are determined as a trade off between consumption and investment among an annuity, a risky and a risk-free asset. Computational results are provided to illustrate the practical implications of the framework.     

Subgradient optimization applied to a discrete nonlinear problem in engineering design

The particular application considered here is the design of relief-header systems, involving compressible fluid flow through tree-networks. The flowrates are specified, and the design problem involves the choice of discrete pipe sizes to minimize total cost while satisfying pressure-drop constraints, which are highly nonlinear. The problem is solved in two stages. Firstly the problem of obtaining the optimal set of continuous pipe sizes is addressed; it turns out that a dual formulation provides and extremely rapid solution. Next, a subgradient optimization procedure is used on the dual in order to solve for the discrete pipe sizes. Networks of up to 78 paths and 205 sections, each involving 50 discrete pipe sizes, have been solved.     

Optimal investment, consumption and retirement choice problem with disutility and subsistence consumption constraints

In this paper we consider a general optimal consumption-portfolio selection problem of an infinitely-lived agent whose consumption rate process is subject to subsistence constraints before retirement. That is, her consumption rate should be greater than or equal to some positive constant before retirement. We integrate three optimal decisions which are the optimal consumption, the optimal investment choice and the optimal stopping problem in which the agent chooses her retirement time in one model. We obtain the explicit forms of optimal policies using a martingale method and a variational inequality arising from the dual function of the optimal stopping problem. We treat the optimal retirement time as the first hitting time when her wealth exceeds a certain wealth level which will be determined by a free boundary value problem and duality approaches. We also derive closed forms of the optimal wealth processes before and after retirement. Some numerical examples are presented for the case of constant relative risk aversion (CRRA) utility class.     

Optimal and robust contracts for a risk-constrained principal

The theory of risk measurement has been extensively developed over the past ten years or so, but there has been comparatively little effort devoted to using this theory to inform portfolio choice. One theme of this paper is to study how an investor in a conventional log-Brownian market would invest to optimize expected utility of terminal wealth, when subjected to a bound on his risk, as measured by a coherent law-invariant risk measure. Results of Kusuoka lead to remarkably complete expressions for the solution to this problem. The second theme of the paper is to discuss how one would actually manage (not just measure) risk. We study a principal/agent problem, where the principal is required to satisfy some risk constraint. The principal proposes a compensation package to the agent, who then optimises selfishly ignoring the risk constraint. The principal can pick a compensation package that induces the agent to select the principal’s optimal choice.     

Independence of irrelevant expansions

Nash characterized the only bargaining solution to satisfy a well-known list of axioms. Independence of Irrelevant Alternatives states invariance of the solution outcome under certain contractions of the bargaining problem. A dual of this axiom is proposed here, stating invariance under certainexpansions of the bargaining problem andNash's solution is characerized by substituting this axiom for IIA in Nash's original list. After a transposition from the domain of bargaining solutions to the domain of choice rules, and a weakening of Invariance with respect to Positive Affine Transformations toTranslation Invariance, this new list of axioms is shown to characterizeUtilitarian rules.     

The proportional solution for rights problems

Recently there have been several studies to provide axiomatic characterizations of solutions to rights problems. However, these studies do not give a satisfactory answer to the question why the proportional solution is the most widely used. This is the question addressed in this paper. To that purpose, we adopt the axiomatic approach; we suggest a set of axioms which a desirable solution should satisfy and we show that the proportional solution is the only solution to satisfy these axioms. Our main axioms are no advantageous reallocation and additivity. A solution satisfies no advantageous reallocation if no subgroup of claimants ever benefits by transferring parts of their claims between themselves. A solution satisfies additivity if it yields the same allocation whether the total estate is divided at once or in several steps.     

Application of fuzzy compromise solution method for fit concept selection

The modern manufacturing environment is highly turbulent so as to satisfy the dynamic needs of customers’. To enable the achievement of competitiveness in this complex business environment, newer manufacturing strategies have been introduced for enabling waste elimination and enhancing flexibility and responsiveness of systems. Fit manufacturing is a competitive manufacturing paradigm which includes lean and agile systems coupled with sustainable benefits. This article presents a study in which the concept selection in fit environment was formulated as Multi Criteria Decision Making (MCDM) problem and solved using fuzzy based compromise solution method, Vlsekriterijumska Optimizacija I Kompromisno Resenje (VIKOR). The selected concept design of automotive component was subjected to implementation in the case organisation.     

Optimal investment, stochastic labor income and retirement

We address an optimal consumption-investment-retirement problem with stochastic labor income. We study the Merton problem assuming that the agent has to take four different decisions: the retirement date which is irreversible; the labor and the consumption rate and the portfolio decision before retirement. After retirement the agent only chooses the portfolio and the consumption rate. We confirm some classical results and we show that labor, portfolio and retirement decisions interact in a complex way depending on the spanning opportunities.     

Longevity-linked assets and pre-retirement consumption/portfolio decisions

We solve the consumption/investment problem of an agent facing a stochastic mortality intensity. The investment set includes a longevity-linked asset, as a derivative on the force of mortality. In a complete and frictionless market, we derive a closed form solution when the agent has Hyperbolic Absolute Risk Aversion preferences and a fixed financial horizon. Our calibrated numerical analysis on US data shows that individuals optimally invest a large fraction of their wealth in longevity-linked assets in the pre-retirement phase, because of their need to hedge against stochastic fluctuations in their remaining life-time at retirement.     

Topology and Geometry Optimization of Branched Sheet Metal Products

In order to optimize branched sheet metal profiles consisting of several chambers, decisions concerning topology and geometry have to be made. This leads to a problem entailing discrete and nonlinear features. We describe an integrated approach combining both aspects. The underlying idea is to use a branch-and-bound algorithm. In each node of the branch-and-bound tree, a nonlinear optimization problem has to be solved. We describe how the branch-and-bound tree is constructed, i.e., how the topology decision can be classified in a meaningful way. Moreover, we explain how to approach the nonlinear optimization problem arising in the nodes of the tree. We conclude by presenting a numerical example. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Joint optimization of product family configuration and scaling design by Stackelberg game

Product family design is generally characterized by two types of approaches: module-based and scale-based. While the former aims to enable product variety based on module configuration, the latter is to variegate product design by scaling up or down certain design parameters. The prevailing practice is to treat module configuration and scaling design as separate decisions or aggregate two design problems as a single-level, all-in-one optimization problem. In practice, optimization of scaling variables is always enacted within a specific modular platform; and meanwhile an optimal module configuration depends on how design parameters are to be scaled. The key challenge is how to deal with explicitly the coupling of these two design optimization problems.     

An extension of the Clark–Haussmann formula and applications

ABSTRACT

This work considers a financial market stochastic model where the uncertainty is driven by a multidimensional Brownian motion. The market price of the risk process makes the transition between real world probability measure and risk neutral probability measure. Traditionally, the martingale representation formulas under the risk neutral probability measure require the market price of risk process to be bounded. However, in several financial models the boundedness assumption of the market price of risk fails; for example a financial market model with the market price of risk following an Ornstein–Uhlenbeck process. This work extends the Clark–Haussmann representation formula to underlying stochastic processes which fail to satisfy the standard requirements. Our methodology is classical, and it uses a sequence of mollifiers. Our result can be applied to hedging and optimal investment in financial markets with unbounded market price of risk. In particular, the mean variance optimization problem can be addressed within our framework.