Narrow Results

This paper studies comparative static effects under uncertainty when investors face a portfolio decision problem with both an endogenous risk and a background risk. Since the security market is complex, there exists situation where security return and background asset return are given by experts’ estimates when they cannot be reflected by historical data. Focusing on such a situation, an uncertain mean-chance model with background risk for optimal portfolio selection is developed, in which the use of chance of portfolio return failing to reach the threshold can help investors easily determine their tolerance toward risk and thus facilitate a decision making. Then we analyze the solution of the programming problem under different threshold return level, i.e., how different degrees of threshold return will affect allocation between risky asset and risk-free asset. Furthermore, we discuss the effects of changes in mean and standard deviation of risky asset and background asset on investment decisions when security return and background asset return follow normal uncertainty distributions. Finally, a real portfolio selection example is given as illustration.

The indeterminacy of financial markets leads investors to face different types of security returns. Usually, security returns are assumed to be random variables when sufficient transaction data are available. If data are missing, they can be regarded as uncertain variables. However, uncertainty and randomness coexist. In this situation, chance theory is the main tool to deal with this complex phenomenon. This paper investigates the conditional value at risk (CVaR) of uncertain random variables and its application to portfolio selection. First, we define the CVaR of uncertain random variables and discuss some of its mathematical properties. Then, we propose an uncertain random simulation to approximate the CVaR. Next, we define the inverse function of the CVaR of uncertain random variables, as well as a computational procedure. As an application in finance, we establish uncertain random mean-CVaR portfolio selection models. We also perform a numerical example to illustrate the applicability of the proposed models. Finally, we numerically compare the mean-CVaR models with the mean-variance models with respect to the optimal investment strategy.

Asset allocation is one of the most important and also challenging issues in finance. In this paper using level crossing analysis we introduce a new approach for portfolio selection. We introduce a portfolio index that is obtained based on minimizing the waiting time to receive known return and risk values. By the waiting time, we mean time that a special level is observed in average. The advantage of this approach is that the investors are able to set their goals based on gaining return and knowing the average waiting time and risk value at the same time. As an example we use our model for forming portfolio of stocks in Tehran Stock Exchange (TSE).

In this paper, we present a method for portfolio selection based on the consideration on deformed exponentials in order to generalize the methods based on the gaussianity of the returns in portfolio, such as the Markowitz model. The proposed method generalizes the idea of optimizing mean-variance and mean-divergence models and allows a more accurate behavior for situations where heavy-tails distributions are necessary to describe the returns in a given time instant, such as those observed in economic crises. Numerical results show the proposed method outperforms the Markowitz portfolio for the cumulated returns with a good convergence rate of the weights for the assets which are searched by means of a natural gradient algorithm.

This paper studies a new strategy for selecting portfolios in the stock market. The strategy is inspired by two streams of previous work: (1) work on universalization of strategies for portfolio selection, which began with Thomas Cover's work on constant rebalanced portfolios, published in 1991,⁴ and (2) more general work on universalization of online algorithms,^17,21,23,30 especially Vladimir Vovk's work on the aggregating algorithm and Markov switching strategies.³² The proposed investment strategy achieves asymptotically the same exponential rate of growth as the portfolio that turns out to be best expost in the long run and does not require any underlying statistical assumptions on the nature of the stock market.

Owing to the fluctuations in the financial markets, many financial variables such as expected return, volatility, or exchange rate may occur imprecisely. But many portfolio selection models consider precise input of these values. Therefore, this paper studies a multiobjective international asset allocation problem under fuzzy environment. In our portfolio selection model, both of the return risk and the exchange risk are considered. The coefficient matrices in the objectives and constraints and the decision value are considered as fuzzy variables. The calculation of the portfolio and efficient frontier is derived by considering the exchange risk in the fuzzy environment. An empirical study is performed based on a portfolio of six securities denominated in six different currencies, i.e., USD, EUR, JPY, CNY, HKD, and GBP. The α-level closed interval portfolio and the fuzzy efficient frontier are obtained with different values of α ∈ (0, 1]. The empirical results indicate that the fuzzy asset selection method is a useful tool for dealing with the imprecise problem in the real world.

Optimal control is an important field of study both in theory and in applications. Based on uncertainty theory, an expected value model of uncertain optimal control problem was studied by Zhu. In this paper, an optimistic value model for uncertain optimal control problem is investigated. Applying Bellman's principle of optimality, the principle of optimality for the model is presented. And then the equation of optimality is obtained for the optimistic value model of uncertain optimal control. Finally, a portfolio selection problem is solved by this equation of optimality.

In the traditional decision theory, choice with undetermined consequence is usually regarded as random variable, which usually describes objective uncertainty. This paper first considers the human uncertainty in making decisions, and employs uncertain variable to describe the choice. Utility function is also employed in the paper, and expected utility is introduced as a criterion to rank the choices. At last, in order to illustrate the uncertain decision making method, a portfolio selection problem is considered.

This paper provides an introduction to how, on the basis of concepts from fuzzy logic, a model of asset allocation can be constructed which can represent and aggregate all the relevant quantitative and qualitative features of an investment plan realistically and in this way attains comparatively good recommendations like an expert. All calculation steps are carried out in a transparent and reproducible manner. In order to clarify the approach and the advantages of the procedure, a pilot model is developed. This supports the advisor with the asset allocation, by first analysing the features of the investment goal and the market expectations and then evaluating the merits of several investment strategies as well as displaying the steps towards their evaluation in a comprehensible manner. Based on case studies, the results of the pilot model are compared with known good recommendations from an investigation of Stiftung Warentest on the quality of advice in banks.

Investors usually invest not only in risky assets but also in risk-free assets and face not only portfolio risk but also background risk. This paper discusses an uncertain portfolio selection problem in risky assets and risk-free assets with monotone increasing multiplicative background risk (MBR), which is prevalent but less research has been done. To do so, we first propose an uncertain mean-risk index model based on uncertainty theory where the security return and MBR are regarded as uncertain variables and give the deterministic form of the model. Then for further analysis, we discuss the critical constraint and optimality condition of the model. Based on the discussion, we study the influence of uncertain MBR on the investors’ decisions. Finally, we provide the case analysis to illustrate the application of our method and the analysis results.

We propose a new framework to measure the risk of a single asset and of a portfolio of financial assets which takes the agent's investment horizon into account. The methodology is based on the moderate and large deviations theory in its simplest form. We show how it can be used to select optimal portfolios given investors' planning horizons and preferences for fatter right or left tails. For practical purposes, we introduce a new parameter, the "dilation exponent" α to characterize asset returns' distributions beyond the information contained in the mean-variance framework. We estimate α for Swiss individual stocks and for MSCI country and sector stock market indices. Finally, we show how to use the dilation exponent in conjunction with Sharpe's ratio for portfolio allocation purposes.

A quadratic discrete time probabilistic model, for optimal portfolio selection, under risk constraint, is introduced in the context of (re-) insurance and finance. The portfolio is composed of contracts with arbitrary underwriting and maturity times. For positive values of underwriting levels, the expected value of the accumulated final result is optimized under constraints on its variance and on annual Returns On Equity. Existence of a unique solution is proved and a Lagrangian formalism is given. An effective method for solving the Euler-Lagrange equations is developed. The approximate determination of the multipliers is discussed. This basic model, which can include both assets and liabilities, is an important building block for more general models, with constraints also on non-solvency probabilities, market-shares, short-fall distributions and Values at Risk.

This paper discusses and analyzes risk measure properties in order to understand how a risk measure has to be used to optimize the investor's portfolio choices. In particular, we distinguish between two admissible classes of risk measures proposed in the portfolio literature: safety-risk measures and dispersion measures. We study and describe how the risk could depend on other distributional parameters. Then, we examine and discuss the differences between statistical parametric models and linear fund separation ones. Finally, we propose an empirical comparison among three different portfolio choice models which depend on the mean, on a risk measure, and on a skewness parameter. Thus, we assess and value the impact on the investor's preferences of three different risk measures even considering some derivative assets among the possible choices.

This paper is devoted to the application of the Independent Component Analysis (ICA) methodology to the problem of selecting portfolio strategies, so as to provide against extremal movements in financial markets. A specific ICA model for describing the extreme fluctuations of asset prices is introduced, stipulating that the distributions of the ICs are heavy tailed (i.e., with power law behavior at infinity). An inference method based on conditional maximum likelihood estimation is proposed for our model, which permits to determine practically optimal investment strategies with respect to extreme risk. Empirical studies based on this modeling are carried out to illustrate our approach.

Portfolio optimization under downside risk is of crucial importance to asset managers. In this article we consider one such particular measure given by the notion of Capital at Risk (CaR), closely related to Value at Risk. We consider portfolio optimization with respect to CaR in the Black-Scholes setting with time dependent parameters and investment strategies, i.e., continuous-time portfolio optimization. We review the results from our previous work in unconstrained portfolio optimization, and then investigate and solve the corresponding problems with the additional constraint of no-short-selling. Analytical formulae are derived for the optimal strategies, and numerical examples are presented.

We study the Markowitz portfolio selection problem with unknown drift vector in the multi-dimensional framework. The prior belief on the uncertain expected rate of return is modeled by an arbitrary probability law, and a Bayesian approach from filtering theory is used to learn the posterior distribution about the drift given the observed market data of the assets. The Bayesian Markowitz problem is then embedded into an auxiliary standard control problem that we characterize by a dynamic programming method and prove the existence and uniqueness of a smooth solution to the related semi-linear partial differential equation (PDE). The optimal Markowitz portfolio strategy is explicitly computed in the case of a Gaussian prior distribution. Finally, we measure the quantitative impact of learning, updating the strategy from observed data, compared to nonlearning, using a constant drift in an uncertain context, and analyze the sensitivity of the value of information with respect to various relevant parameters of our model.

We study a dynamic mean-variance portfolio selection problem subject to possible limit of market risk. Three measures of market risk are considered: value-at-risk, expected shortfall, and median shortfall. They are all calculated in a dynamic consistent sense. After applying the technique of delta-normal approximation, we can explicitly solve for the optimal solution and calculate the economic loss brought by the risk budget constraint. With the analytical results obtained, influential factors of economic loss are then explored by which some guidelines on trading practice are proposed. The guidelines are independent of risk measures, and are valuable to both institutions and regulators, for they suggest that an institutional investor would spontaneously obey good investment discipline to avoid potential impact of risk constraint. This result meets the purpose of external regulation from the perspective of market discipline.

The purpose of this study is to apply polynomial goal programming to establish a new portfolio selection model that considers the tradeoffs between expected return and Value-at-Risk (VaR) of portfolios and the flexibility of incorporating investor's preferences. The historical data of 10 international stock markets of Pacific Rim countries were used in the empirical analysis. The results showed that the proposed model demonstrated the ability to resolve the problems of a traditional asset allocation model. The validity and fitness of the proposed model were confirmed.

The extensible, structural and validated nature of XML provides standard data representation for efficient data interchange among diverse information resources available on the Web. Therefore, it leads to its growing recognition in e-commerce and Internet-based information exchange. In this paper, we stress the adoption of XML technology in developing efficient and flexible Web-enabled decision support systems. Based on a case study for portfolio selection systems, we explore the design issues in applying XML to overcome the heterogeneity of data exchange and sharing of various portfolio optimization models.

Simulation optimization is providing solutions to important practical problems previously beyond reach. This paper explores how new approaches are significantly expanding the power of simulation optimization for managing risk. Recent advances in simulation optimization technology are leading to new opportunities to solve problems more effectively. Specifically, in applications involving risk and uncertainty, simulation optimization surpasses the capabilities of other optimization methods not only in the quality of solutions but also in their interpretability and practicality. In this paper, we demonstrate the advantages of using a simulation optimization approach to tackle risky decisions, by showcasing the methodology on two popular applications from the areas of finance and business process design.