TRACTABLE ROBUST EXPECTED UTILITY AND RISK MODELS FOR PORTFOLIO OPTIMIZATION

Expected utility models in portfolio optimization are based on the assumption of complete knowledge of the distribution of random returns. In this paper, we relax this assumption to the knowledge of only the mean, covariance, and support information. No additional restrictions on the type of distribution such as normality is made. The investor’s utility is modeled as a piecewise‐linear concave function. We derive exact and approximate optimal trading strategies for a robust (maximin) expected utility model, where the investor maximizes his worst‐case expected utility over a set of ambiguous distributions. The optimal portfolios are identified using a tractable conic programming approach. Extensions of the model to capture asymmetry using partitioned statistics information and box‐type uncertainty in the mean and covariance matrix are provided. Using the optimized certainty equivalent framework, we provide connections of our results with robust or ambiguous convex risk measures, in which the investor minimizes his worst‐case risk under distributional ambiguity. New closed‐form results for the worst‐case optimized certainty equivalent risk measures and optimal portfolios are provided for two‐ and three‐piece utility functions. For more complicated utility functions, computational experiments indicate that such robust approaches can provide good trading strategies in financial markets.     

On utility maximization under model uncertainty in discrete‐time markets

We study the problem of maximizing terminal utility for an agent facing model uncertainty, in a frictionless discrete‐time market with one safe asset and finitely many risky assets. We show that an optimal investment strategy exists if the utility function, defined either on the positive real line or on the whole real line, is bounded from above. We further find that the boundedness assumption can be dropped, provided that we impose suitable integrability conditions, related to some strengthened form of no‐arbitrage. These results are obtained in an alternative framework for model uncertainty, where all possible dynamics of the stock prices are represented by a collection of stochastic processes on the same filtered probability space, rather than by a family of probability measures.     

Markov chains under nonlinear expectation

In this paper, we consider continuous‐time Markov chains with a finite state space under nonlinear expectations. We define so‐called Q‐operators as an extension of Q‐matrices or rate matrices to a nonlinear setup, where the nonlinearity is due to model uncertainty. The main result gives a full characterization of convex Q‐operators in terms of a positive maximum principle, a dual representation by means of Q‐matrices, time‐homogeneous Markov chains under convex expectations, and a class of nonlinear ordinary differential equations. This extends a classical characterization of generators of Markov chains to the case of model uncertainty in the generator. We further derive an explicit primal and dual representation of convex semigroups arising from Markov chains under convex expectations via the Fenchel–Legendre transformation of the generator. We illustrate the results with several numerical examples, where we compute price bounds for European contingent claims under model uncertainty in terms of the rate matrix.     

The decision processes of innovative communicators and other adopters

Based on the nature of their involvement with the target product category three market segments of consumers of fashion innovations are identified. It is hypothesised that each segment of consumers should use a different decision process when adopting an innovation. The major findings of this study are that the more innovative consumers used a less extensive pattern of decision making activity than consumers who were either less involved with the product category or were concerned about how the purchase would effect their perceived social status. These findings suggest that involvement with the category is different to involvement in the decision making process, and that the latter is somewhat contingent on situational factors.Thanks are expressed to John Rossiter, Judy Zaichkowsky, and the editor and reviewers for their comments on an earlier draft.     

Portfolio Optimization and Martingale Measures

The paper studies connections between risk aversion and martingale measures in a discrete-time incomplete financial market. An investor is considered whose attitude toward risk is specified in terms of the index b of constant proportional risk aversion. Then dynamic portfolios are admissible if the terminal wealth is positive. It is assumed that the return (risk) processes are bounded. Sufficient (and nearly necessary) conditions are given for the existence of an optimal dynamic portfolio which chooses portfolios from the interior of the set of admissible portfolios. This property leads to an equivalent martingale measure defined through the optimal dynamic portfolio and the index 0 < b ≤ 1. Moreover, the option pricing formula of Davis is given by this martingale measure. In the case of b = 1; that is, in the case of the log-utility, the optimal dynamic portfolio defines the numéraire portfolio.     

Superreplication with proportional transaction cost under model uncertainty

We consider a discrete‐time financial market with proportional transaction cost under model uncertainty, and study a superreplication problem. We recover the duality results that are well known in the classical dominated context. Our key argument consists in using a randomization technique together with the minimax theorem to convert the initial problem to a frictionless problem on an enlarged space. This allows us to appeal to the techniques and results of Bouchard and Nutz to obtain the duality result.     

A random coefficients mixture hidden Markov model for marketing research

The hidden Markov model (HMM) provides a framework to model the time-varying effects of marketing mix variables. When employed in a panel data context, it is important to properly account for unobserved heterogeneity across individuals. We propose a new random coefficients mixture HMM (RCMHMM) that allows for flexible patterns of unobserved heterogeneity in both the state-dependent and transition parameters. The RCMHMM nests all HMMs found in the marketing literature. Results of two simulation studies demonstrate that 1) averaging across a large number of different data generating processes, the RCMHMM outperforms all its nested versions using both in-sample and out-of-sample performance and 2) the RCMHMM is more robust than its nested versions when underlying model assumptions are violated. In addition, we apply the RCMHMM to an empirical application where we examine the effectiveness of in-game promotions in increasing the short-term demand for Major League Baseball (MLB) attendance. We find that the effectiveness of four promotional categories varies over the course of the season and across teams and that the RCMHMM performs best.     

Merger and acquisition evaluation and decision making model

Based on three merger and acquisition (M&A) methods and applying multiple-criteria decision making, the purpose of this paper is to establish an M&A evaluation model. The decision making trial and evaluation laboratory (DEMATEL) results show that the three business M&A methods possess interactive effect and self-feedback relationships. This study utilizes the analytic network process to calculate the weights of seven evaluation criteria; expected stock dividend is ranked as the most important criterion, followed by stock price/earnings per share, stock dividend growth, sales/market capitalization ratio, discount rate, replacement value, and liquidation value. This study uses Vlsekriterijumska Optimizacija I Kompromisno Resenje (VIKOR) to evaluate the performance of three Taiwanese banks. The results show that Bank B is the best M&A investment choice. Finally, the study establishes a comprehensive M&A decision making evaluation model.     

Decision making and decision aiding: Defining the process,it representations,and support

We present a formalized account of decision making as a multistep process that involves several classes of participating entities. The purpose of this article is to lay the foundations for a conceptual framework in which decision support systems can be placed. A series of increasingly formal representations of the decision problem are developed, from a mental model conceived by the decision maker to a knowledge base that may be used in a decision support system. The reformulations of the decision problem lead us to contemplate different forms of support: for mental models, for formal models (this includes supporting measurement and representation), for solution, and for communication.     

Backward SDEs for control with partial information

This paper considers a non‐Markov control problem arising in a financial market where asset returns depend on hidden factors. The problem is non‐Markov because nonlinear filtering is required to make inference on these factors, and hence the associated dynamic program effectively takes the filtering distribution as one of its state variables. This is of significant difficulty because the filtering distribution is a stochastic probability measure of infinite dimension, and therefore the dynamic program has a state that cannot be differentiated in the traditional sense. This lack of differentiability means that the problem cannot be solved using a Hamilton–Jacobi–Bellman equation. This paper will show how the problem can be analyzed and solved using backward stochastic differential equations, with a key tool being the problem's dual formulation.     

Effectuation under risk and uncertainty: A simulation model

Effectuation was first proposed as an expert entrepreneur's decision-making framework under uncertainty, but the applications of effectuation beyond the condition of uncertainty have seen less attention. Using an agent-based simulation model, this paper investigates the effectiveness of effectuation relative to causation in uncertain and risky contexts. The simulation overcomes the shortcomings of think aloud protocols typically used in effectuation research. The results suggest that effectuation outperforms causation in both risky and uncertain contexts until the entrepreneur can predict the future correctly > 75% of the time. This suggests expanding the boundary of effectuation from uncertainty to whenever predicting the future is challenging.     

A multiobjective decision support system for multiresource forest management

A multiobjective and/or multiperson decision support system for analyzing multiresource forest management problems is developed in this paper. The procedure includes formulating the problem in a multiobjective and group decision making framework, and solving it using two solution techniques which consist of a distance-based compromise programming (CP) and a cooperative game theoretic approach of the Nash equilibrium type. The problem consists of five forest resources management objective functions to be maximized. Solving the problem using the two solution techniques enables determining a satisfactory compromise solution of the five forest resource management objectives. Sensitivity analysis of the two techniques shows compromise programming to be more sensitive to changes in the weight and the p-parameter of the technique while the cooperative game theoretic approach is relatively robust with respect to changes in the worst utility set.     

基于多属性模糊决策的行为投资组合优化模型

Simon认为经典决策理论的假定过分地严格,在实际中往往难以满足。运用上、下偏矩的方法来估计未来财富不低于渴求水平的概率,并基于多属性模糊决策方法构建两个心理帐户的行为投资组合优化模型。模型中融入了不同质投资者的真实情感、信念及认知状态,实证分析的结果表明该模型具有很强的实用性和包容性。     

基于偏度的多期证券投资组合模型研究

在考虑资产收益率分布中正的偏度水平前提下,以风险价值VaR为约束条件,并引入非线性交易费用、税收等市场摩擦因素,建立以累积偏度最大为目标函数的多期投资组合优化模型,用罚函数法和PSO算法结合求解此模型,并给出实证分析。考虑到在买卖资产风险时交易费用等对投资收益的影响,投资者应该在每一期都对其资产组合进行调整分析,确保在每一期的开始都建立起符合需要的最优资产组合,这对投资者的连续投资行为具有一定的指导意义。     

OPTIONED PORTFOLIO SELECTION: MODELS AND ANALYSIS

The mean‐variance model of Markowitz and many of its extensions have been playing an instrumental role in guiding the practice of portfolio selection. In this paper we study a mean‐variance formulation for the portfolio selection problem involving options. In particular, the portfolio in question contains a stock index and some European style options on the index. A refined mean‐variance methodology is adopted in our approach to formulate this problem as multistage stochastic optimization. It turns out that there are two different solution techniques, both lead to explicit solutions of the problem: one is based on stochastic programming and optimality conditions, and the other one is based on stochastic control and dynamic programming. We introduce both techniques, because their strengths are very different so as to suit different possible extensions and refinements of the basic model. Attention is paid to the structure of the optimal payoff function, which is shown to possess rich properties. Further refinements of the model, such as the request that the payoff should be monotonic with respect to the index, are discussed. Throughout the paper, various numerical examples are used to illustrate the underlying concepts.     

OPTIMAL INVESTMENT IN CREDIT DERIVATIVES PORTFOLIO UNDER CONTAGION RISK

We consider the optimal portfolio problem of a power investor who wishes to allocate her wealth between several credit default swaps (CDSs) and a money market account. We model contagion risk among the reference entities in the portfolio using a reduced‐form Markovian model with interacting default intensities. Using the dynamic programming principle, we establish a lattice dependence structure between the Hamilton‐Jacobi‐Bellman equations associated with the default states of the portfolio. We show existence and uniqueness of a classical solution to each equation and characterize them in terms of solutions to inhomogeneous Bernoulli type ordinary differential equations. We provide a precise characterization for the directionality of the CDS investment strategy and perform a numerical analysis to assess the impact of default contagion. We find that the increased intensity triggered by default of a very risky entity strongly impacts size and directionality of the investor strategy. Such findings outline the key role played by default contagion when investing in portfolios subject to multiple sources of default risk.     

A model and case for supporting participatory public decision making in e-democracy

In this paper, focusing on participatory public decision making processes, I propose a framework for group support systems and discuss related research issues. As a case illustrating the feasibility of participatory public decision making, I present the participatory budgeting experience in Porto Alegre, Brazil. The case is analyzed based on the proposed framework.     

Integrated consumer shopping decision model: A Japanese online supermarket context

Abstract

Online shopping is not a new marketing channel but has been growing tremendously throughout Japan. The rapid growth of Internet technology has enabled the Japanese to break away from their conservative culture and embark on different shopping experiences by shopping online. With the growing importance of online reviews to promote one’s business, Japanese online supermarkets are looking for ways to increase consumer-generated content. The purpose of this study is to investigate Japanese repeat online consumers and the antecedents that encourage them to review their shopping experiences, including the supermarket website they used and product availability in the online supermarket. It was found that online supermarkets must focus on establishing confidence with their repeat online consumers if they desire to increase the electronic word of mouth (e-WOM) of their online supermarket. Implications are discussed in relation to online supermarkets and repeat consumers’ intentions to review their online shopping experiences.