Admissible investment strategies in continuous trading

We consider a situation where relative prices of assets may change continuously and also have discrete jumps at random time points. The problem is the one of portfolio optimization. If the utility function used is the logarithm, we first argue that an optimal investment plan exists. Secondly, we show that any such plan has a certain optimality property known to hold also in discrete time models. Moreover, we show that this optimality criterion can be simplified significantly. In particular we show how admissibility can be related directly to observable characteristics of the investment strategy.     

The optimal resource portfolio under consumer choice and demand risk for vertically differentiated products

We study the optimal resource portfolio of a firm that sells two vertically differentiated products and utilizes resource flexibility and responsive pricing. We model this decision problem as a two-stage stochastic programming problem with recourse: In the first stage, the firm determines its resource mix and capacities so as to maximize the expected profit under demand uncertainty; in the second stage, uncertainty is resolved and the firm determines its production and pricing decision, constrained by its investment decision. We show that the objective function of this decision problem is not well-behaved (ie, it may have multiple local maxima). Using the concept of Pareto dominance, we reduce the feasible investment region, without loss of optimality, to one in which the objective function is well-behaved everywhere. This reduction allows us to derive the necessary and sufficient conditions for the optimal capacity decision and to gain insights.     

Decision Analysis in Venture Capital

A number of decision criteria are evaluated in the context of a portfolio of investments in venture capital.The essence of this activity is that it is a sequential decision problem with stochastic time intervals between decisions, where the choice is to make an investment or not. The pay-off from the investment is a payment of random magnitude after a time interval of random length.Some of the criteria used in security portfolio analysis are adapted for use in this context and compared with simpler criteria. Due to the typically risky nature of these investments, the level of information about the investment is kept to a realistic level.The results of simulation experiments demonstrate effectively the benefit of using rational decision criteria, but that there is surprisingly little difference between the effects of these criteria.     

Optimal investment consumption model with a higher interest rate for borrowing

This paper considers a consumption and investment decision problem with a higher interest rate for borrowing as well as the dividend rate. Wealth is divided into a riskless asset and risky asset with logrithmic Erownian motion price fluctuations. The stochastic control problem of maximizating expected utility from terminal wealth and consumption is studied. Equivalent conditions for optimality are obtained. By using duality methods ,the existence of optimal portfolio consumption is proved,and the explicit solutions leading to feedback formulae are derived for deteministic coefficients.     

Time-consistent investment strategy under partial information

This paper considers a mean–variance portfolio selection problem under partial information, that is, the investor can observe the risky asset price with random drift which is not directly observable in financial markets. Since the dynamic mean–variance portfolio selection problem is time inconsistent, to seek the time-consistent investment strategy, the optimization problem is formulated and tackled in a game theoretic framework. Closed-form expressions of the equilibrium investment strategy and the corresponding equilibrium value function under partial information are derived by solving an extended Hamilton–Jacobi–Bellman system of equations. In addition, the results are also given under complete information, which are need for the partial information case. Furthermore, some numerical examples are presented to illustrate the derived equilibrium investment strategies and numerical sensitivity analysis is provided.     

Log-Optimal Portfolios with Memory Effect

ABSTRACT

In portfolio optimization a classical problem is to trade with assets so as to maximize some kind of utility of the investor. In our paper this problem is investigated for assets whose prices depend on their past values in a non-Markovian way. Such models incorporate several features of real price processes better than Markov processes do. Our utility function is the widespread logarithmic utility, the formulation of the model is discrete in time. Despite the problem being a well-known one, there are few results where memory is treated systematically in a parametric model. Our algorithm is optimal and this optimality is guaranteed for a rich class of model specifications. Moreover, the algorithm runs online, i.e., the optimal investment is achieved in a day-by-day manner, using simple numerical integration, without Monte-Carlo simulations. Theoretical results are demonstrated by numerical experiments as well.     

A multicriteria optimization model of portfolio rebalancing with transaction costs in fuzzy environment

In this paper we propose multicriteria credibilistic framework for portfolio rebalancing (adjusting) problem with fuzzy parameters considering return, risk and liquidity as key financial criteria. The portfolio risk is characterized by a risk curve that represents each likely loss of the portfolio return and the corresponding chance of its occurrence rather than a single pre-set level of the loss. Furthermore, we consider an investment market scenario where, at the end of a typical time period, the investor would like to modify his existing portfolio by buying and/or selling assets in response to changing market conditions. We assume that the investor pays transaction costs based on incremental discount schemes associated with the buying and/or selling of assets, which are adjusted in the net return of the portfolio. A hybrid intelligent algorithm that integrates fuzzy simulation with a real-coded genetic algorithm is developed to solve the portfolio rebalancing (adjusting) problem. The proposed solution approach is useful particularly for the cases where fuzzy parameters of the problem are characterized by general functional forms.     

Dynamic multi-criteria evaluation of co-evolution strategies for solving stock trading problems

Risk and return are interdependent in a stock portfolio. To achieve the anticipated return, comparative risk should be considered simultaneously. However, complex investment environments and dynamic change in decision making criteria complicate forecasts of risk and return for various investment objects. Additionally, investors often fail to maximize their profits because of improper capital allocation. Although stock investment involves multi-criteria decision making (MCDM), traditional MCDM theory has two shortfalls: first, it is inappropriate for decisions that evolve with a changing environment; second, weight assignments for various criteria are often oversimplified and inconsistent with actual human thinking processes.In 1965, Rechenberg proposed evolution strategies for solving optimization problems involving real number parameters and addressed several flaws in traditional algorithms, such as their use of point search only and their high probability of falling into optimal solution area. In 1992, Hillis introduced the co-evolutionary concept that the evolution of living creatures is interactive with their environments (multi-criteria) and constantly improves the survivability of their genes, which then expedites evolutionary computation. Therefore, this research aimed to solve multi-criteria decision making problems of stock trading investment by integrating evolutionary strategies into the co-evolutionary criteria evaluation model. Since co-evolution strategies are self-calibrating, criteria evaluation can be based on changes in time and environment. Such changes not only correspond with human decision making patterns (i.e., evaluation of dynamic changes in criteria), but also address the weaknesses of multi-criteria decision making (i.e., simplified assignment of weights for various criteria).Co-evolutionary evolution strategies can identify the optimal capital portfolio and can help investors maximize their returns by optimizing the preoperational allocation of limited capital. This experimental study compared general evolution strategies with artificial neural forecast model, and found that co-evolutionary evolution strategies outperform general evolution strategies and substantially outperform artificial neural forecast models. The co-evolutionary criteria evaluation model avoids the problem of oversimplified adaptive functions adopted by general algorithms and the problem of favoring weights but failing to adaptively adjust to environmental change, which is a major limitation of traditional multi-criteria decision making. Doing so allows adaptation of various criteria in response to changes in various capital allocation chromosomes. Capital allocation chromosomes in the proposed model also adapt to various criteria and evolve in ways that resemble thinking patterns.     

Portfolio symmetry and momentum

This paper presents a novel theoretical framework to model the evolution of a dynamic portfolio (i.e., a portfolio whose weights vary over time), considering a given investment policy. The framework is based on graph theory and the quantum probability. Embedding the dynamics of a portfolio into a graph, each node of the graph representing a plausible portfolio, we provide the probabilities for a dynamic portfolio to lie on different nodes of the graph, characterizing its optimality in terms of returns. The framework embeds cross-sectional phenomena, such as the momentum effect, in stochastic processes, using portfolios instead of individual stocks. We apply our methodology to an investment policy similar to the momentum strategy of Jegadeesh and Titman (1993). We find that the strategy symmetry is a source of momentum.     

Capital Asset Pricing Model (CAPM) with drawdown measure

The notion of drawdown is central to active portfolio management. Conditional Drawdown-at-Risk (CDaR) is defined as the average of a specified percentage of the largest drawdowns over an investment horizon and includes maximum and average drawdowns as particular cases. The necessary optimality conditions for a portfolio optimization problem with CDaR yield the capital asset pricing model (CAPM) stated in both single and multiple sample-path settings. The drawdown beta in the CAPM has a simple interpretation and is evaluated for hedge fund indices from the HFRX database in the single sample-path setting. Drawdown alpha is introduced similarly to the alpha in the classical CAPM and is evaluated for the same hedge fund indices. Both drawdown beta and drawdown alpha are used to prioritize hedge fund strategies and to identify instruments for hedging against market drawdowns.     

Quasi‐optimality of the adaptive finite element method for the eigenvalue problem arising from the vibration frequencies of the cavity flow

In this article, we present a posteriori error analysis for the regularization formulation of the eigenvalue problem arising from the vibration frequencies of the cavity flow. The quasi‐optimality of the adaptive finite element method is also proved for the single eigenvalues under the Dörfler's marking strategy without marking the oscillation terms and enforcing the so‐called interior node property. Numerical examples illustrate the quasi‐optimality of the adaptive finite element method. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 900–922, 2015     

Multiobjective optimization using differential evolution for real-world portfolio optimization

Portfolio optimization is an important aspect of decision-support in investment management. Realistic portfolio optimization, in contrast to simplistic mean-variance optimization, is a challenging problem, because it requires to determine a set of optimal solutions with respect to multiple objectives, where the objective functions are often multimodal and non-smooth. Moreover, the objectives are subject to various constraints of which many are typically non-linear and discontinuous. Conventional optimization methods, such as quadratic programming, cannot cope with these realistic problem properties. A valuable alternative are stochastic search heuristics, such as simulated annealing or evolutionary algorithms. We propose a new multiobjective evolutionary algorithm for portfolio optimization, which we call DEMPO??Differential Evolution for Multiobjective Portfolio Optimization. In our experimentation, we compare DEMPO with quadratic programming and another well-known evolutionary algorithm for multiobjective optimization called NSGA-II. The main advantage of DEMPO is its ability to tackle a portfolio optimization task without simplifications, while obtaining very satisfying results in reasonable runtime.     

Multi-period portfolio optimization for asset–liability management with bankrupt control

In this paper, we investigate a multi-period portfolio optimization problem for asset–liability management of an investor who intends to control the probability of bankruptcy before reaching the end of an investment horizon. We formulate the problem as a generalized mean–variance model that incorporates bankrupt control over intermediate periods. Based on the Lagrangian multiplier method, the embedding technique, the dynamic programming approach and the Lagrangian duality theory, we propose a method to solve the model. A numerical example is given to demonstrate our method and show the impact of bankrupt control and market parameters on the optimal portfolio strategy.     

Optimal closing of a pair trade with a model containing jumps

A pair trade is a portfolio consisting of a long position in one asset and a short position in another, and it is a widely used investment strategy in the financial industry. Recently, Ekström, Lindberg, and Tysk studied the problem of optimally closing a pair trading strategy when the difference of the two assets is modelled by an Ornstein-Uhlenbeck process. In the present work the model is generalized to also include jumps. More precisely, we assume that the difference between the assets is an Ornstein-Uhlenbeck type process, driven by a Lévy process of finite activity. We prove a necessary condition for optimality (a so-called verification theorem), which takes the form of a free boundary problem for an integro-differential equation. We analyze a finite element method for this problem and prove rigorous error estimates, which are used to draw conclusions from numerical simulations. In particular, we present strong evidence for the existence and uniqueness of an optimal solution.     

Genetic algorithm-based multi-criteria project portfolio selection

Project portfolio selection is one of the most important decision-making problems for most organizations in project management and engineering management. Usually project portfolio decisions are very complicated when project interactions in terms of multiple selection criteria and preference information of decision makers (DMs) in terms of the criteria importance are taken into consideration simultaneously. In order to solve this complex decision-making problem, a multi-criteria project portfolio selection problem considering project interactions in terms of multiple selection criteria and DMs?? preferences is first formulated. Then a genetic algorithm (GA)-based nonlinear integer programming (NIP) approach is used to solve the multi-criteria project portfolio selection problem. Finally, two illustrative examples are presented for demonstration and verification purposes. Experimental results obtained indicate that the GA-based NIP approach can be used as a feasible and effective solution to multi-criteria project portfolio selection problems.     

随机利率及随机收益保证下的投资策略

考虑随机利率环境及随机收益保证下基金经理的投资组合问题。利用鞅方法,得到了最优投资策略的显性解。结论表明,最优投资策略包括三个部分：投机策略、利率套期保值策略以及随机收益保证的复制策略,且该最优策略等价于将一部分资金投资于确保终端时刻获得最低收益的基准组合,而剩余资金则依照无保证情况下的最优策略进行投资。     

Portfolio selection problems with Markowitz’s mean–variance framework: a review of literature

Since the pioneering work of Harry Markowitz, mean–variance portfolio selection model has been widely used in both theoretical and empirical studies, which maximizes the investment return under certain risk level or minimizes the investment risk under certain return level. In this paper, we review several variations or generalizations that substantially improve the performance of Markowitz’s mean–variance model, including dynamic portfolio optimization, portfolio optimization with practical factors, robust portfolio optimization and fuzzy portfolio optimization. The review provides a useful reference to handle portfolio selection problems for both researchers and practitioners. Some summaries about the current studies and future research directions are presented at the end of this paper.     

Anticipative portfolio optimization under constraints and a higher interest rate for borrowing

We study a stochastic control problem to maximize expected utility from terminal and/or consumption. The novel feature of our work is that the portfolio is allowed to anticipate the future with constraints and a higher interest rate for borrowing. The investor possesses information about the terminal values of the components of the Brownian motion, possibly distorted by ‘noise’. We use the technique from the so-called enlargement of filtrations, to model our problem. General existence results are established for optimal portfolio and consumption strategies. Equivalent conditions for optimality are obtained, and explicit solutions leading to feedback formulae are derived for special utility functions and for deterministic coefficients.     

Valuation and hedging of participating life-insurance policies under management discretion

The valuation and hedging of participating life insurance policies, also known as with-profits policies, is considered. Such policies can be seen as European path-dependent contingent claims whose underlying security is the investment portfolio of the insurance company that sold the policy. The fair valuation of these policies is studied under the assumption that the insurance company has the right to modify the investment strategy of the underlying portfolio at any time. Furthermore, it is assumed that the issuer of the policy does not setup a separate portfolio to hedge the risk associated with the policy. Instead, the issuer will use its discretion about the investment strategy of the underlying portfolio to hedge shortfall risks. In that sense, the insurer’s investment portfolio serves simultaneously as the underlying security and as the hedge portfolio. This means that the hedging problem can not be separated from the valuation problem. We investigate the relationship between risk-neutral valuation and hedging of these policies in complete and incomplete financial markets.     

最小风险组合证券非负投资比例系数的确定

研究非负投资比例系数约束条件下,实现风险最小化的组合证券投资问题.应用罚函数法,对最小风险组合证券的非负投资比例系数进行研究.实例表明:这一方法是可行的、有效的.