An M-ary detection approach for asset allocation

We develop a continuous-time asset allocation model which incorporates both model uncertainty and structural changes in economic conditions. A “dynamic” M-ary detection framework for a continuous-time hidden Markov chain partially observed in a Gaussian process is used to model the price dynamics of the risky asset and the hidden states of an economy. The goal of an investor is to select an optimal asset portfolio mix so as to maximize the expected utility of terminal wealth. Filtering theory is used first to turn the problem into one with complete observations and then to derive M-ary detection filters for the hidden system. The Hamilton-Jacobi-Bellman dynamic programming approach is used to solve the asset allocation problem with complete observations. An explicit solution is obtained for the power utility case.     

Trading a mean-reverting asset: Buy low and sell high

This paper is concerned with an optimal trading (buy and sell) rule. The underlying asset price is governed by a mean-reverting model. The objective is to buy and sell the asset so as to maximize the overall return. Slippage cost is imposed on each transaction. The associated HJB equations (quasi-variational inequalities) are used to characterize the value functions. It is shown that the solution to the original optimal stopping problem can be obtained by solving two quasi-algebraic equations. Sufficient conditions are given in the form of a verification theorem. A numerical example is reported to demonstrate the results.     

Modeling and managing portfolios including listed private equity

Listed private equity (LPE) provides investors with a liquid means of considering private equity in their portfolios. This paper presents a first-order autoregressive Markov-switching model (ARMS) which is able to capture the characteristics of the asset classes bonds, stocks, and LPE, such as heavy tails and autocorrelation. Optimizing a portfolio between bonds, stocks, and LPE shows that an investor benefits from including LPE due to the high diversification effects, which also holds for a very risk-averse investor. Allocating a portfolio with the presented Markov-switching optimization can help to significantly outperform a portfolio which is optimized assuming an underlying geometric Brownian motion (GBM) - even during the financial crisis: The terminal value of a portfolio of a model investor with medium risk aversion was on average 8.7% higher over the three years 2007-2009 than the GBM portfolio.     

An adaptive modeling and asset allocation approach to financial markets based on discrete microstructure model

In previous works, it was verified that the discrete-time microstructure (DTMS) model, which is estimated by training dataset of a financial time series, may be effectively applied to asset allocation control on the following test data. However, if the length of test dataset is too long, prediction capability of the estimated DTMS model may gradually decline due to behavior change of financial market, so that the asset allocation result may become worse on the latter part of test data. To overcome the drawback, this paper presents a semi-on-line adaptive modeling and trading approach to financial time series based on the DTMS model and using a receding horizon optimization procedure. First, a long-interval identification window is selected, and the dataset on the identification window is used to estimate a DTMS model, which will be used to do asset allocation on the following short-term trading interval that is referred to as the trading window. After asset allocation is over on the trading window, the length-fixed identification window is then moved to a new window that includes the previous trading window, and a new DTMS model is estimated by using the dataset on the new identification window. Next, asset allocation continues on the next trading window that follows the previous trading window, and then the modeling and asset allocation process will go on according to the above steps. In order to enhance the flexibility and adaptability of the DTMS model, a comprehensive parameter optimization method is proposed, which incorporates particle swarm optimization (PSO) with Kalman filter and maximum likelihood method for estimating the states and parameters of DTMS model. Based on the adaptive DTMS model estimated on each identification window, an adaptive asset allocation control strategy is designed to achieve optimal control of financial assets. The parameters of the asset allocation controller are optimized by the PSO algorithm on each identification window. Case studies on Hang Seng Index (HSI) of Hong Kong stock exchange and S&P 500 index show that the proposed adaptive modeling and trading strategy can obtain much better asset allocation control performance compared with the parameters-fixed DTMS model.     

Aligning the economic modeling of software reuse with reuse practices

In contrast to current practices where software reuse is applied recursively and reusable assets are tailored trough parameterization or specialization, existing reuse economic models assume that (i) the cost of reusing a software asset depends on its size and (ii) reusable assets are developed from scratch. The contribution of this paper is that it provides modeling elements and an economic model that is better aligned with current practices. The functioning of the model is illustrated in an example. The example also shows how the model can support practitioners in deciding whether it is economically feasible to apply software reuse recursively.     

Extracting Information from Spot Interest Rates and Credit Ratings using Double Higher-Order Hidden Markov Models

Estimating and forecasting the unobservable states of an economy are important and practically relevant topics in economics. Central bankers and regulators can use information about the market expectations on the hidden states of the economy as a reference for decision and policy makings, for instance, deciding monetary policies. Spot interest rates and credit ratings of bonds contain important information about the hidden sequence of the states of the economy. In this paper, we develop double higher-order hidden Markov chain models (DHHMMs) for extracting information about the hidden sequence of the states of an economy from the spot interest rates and credit ratings of bonds. We consider a discrete-state model described by DHHMMs and focus on the qualitative aspect of the unobservable states of the economy. The observable spot interest rates and credit ratings of bonds depend on the hidden states of the economy which are modelled by DHHMMs. The DHHMMs can incorporate the persistent phenomena of the time series of spot interest rates and the credit ratings. We employ the maximum likelihood method and the EM algorithm, namely Viterbi's algorithm, to uncover the optimal hidden sequence of the states of the economy which can be interpreted the “best” estimate of the sequence of the underlying economic states generating the spot interest rates and credit ratings of the bonds. Then, we develop an efficient maximum likelihood estimation method to estimate the unknown parameters in our model. Numerical experiment will be conducted to illustrate the implementation of the model. An erratum to this article can be found at     

Optimal portfolios with regime switching and value-at-risk constraint

We consider the optimal portfolio selection problem subject to a maximum value-at-Risk (MVaR) constraint when the price dynamics of the risky asset are governed by a Markov-modulated geometric Brownian motion (GBM). Here, the market parameters including the market interest rate of a bank account, the appreciation rate and the volatility of the risky asset switch over time according to a continuous-time Markov chain, whose states are interpreted as the states of an economy. The MVaR is defined as the maximum value of the VaRs of the portfolio in a short time duration over different states of the chain. We formulate the problem as a constrained utility maximization problem over a finite time horizon. By utilizing the dynamic programming principle, we shall first derive a regime-switching Hamilton-Jacobi-Bellman (HJB) equation and then a system of coupled HJB equations. We shall employ an efficient numerical method to solve the system of coupled HJB equations for the optimal constrained portfolio. We shall provide numerical results for the sensitivity analysis of the optimal portfolio, the optimal consumption and the VaR level with respect to model parameters. These results are also used to investigating the effect of the switching regimes.     

A Stochastic-Goal Mixed-Integer Programming approach for integrated stock and bond portfolio optimization

We consider a Stochastic-Goal Mixed-Integer Programming (SGMIP) approach for an integrated stock and bond portfolio problem. The portfolio model integrates uncertainty in asset prices as well as several important real-world trading constraints. The resulting formulation is a structured large-scale problem that is solved using a model specific algorithm that consists of a decomposition, warm-start, and iterative procedure to minimize constraint violations. We present computational results and portfolio return values in comparison to a market performance measure. For many of the test cases the algorithm produces optimal solutions, where CPU time is improved greatly.     

Distributing weights under hierarchical clustering: A way in reducing performance breakdown

This paper proposes a clustering asset allocation scheme which provides better risk-adjusted portfolio performance than those obtained from traditional asset allocation approaches such as the equal weight strategy and the Markowitz minimum variance allocation. The clustering criterion used, which involves maximization of the in-sample Sharpe ratio (SR), is different from traditional clustering criteria reported in the literature. Two evolutionary methods, namely Differential Evolution and Genetic Algorithm, are employed to search for such an optimal clustering structure given a cluster number. To explore the clustering impact on the SR, the in-sample and the out-of-sample SR distributions of the portfolios are studied using bootstrapped data as well as simulated paths from the single index market model. It was found that the SR distributions of the portfolios under the clustering asset allocation structure have higher mean values and skewness but approximately the same standard deviation and kurtosis than those in the non-clustered case. Genetic Algorithm is suggested as a more efficient approach than Differential Evolution for the purpose of solving the clustering problem.     

机构投资者的最优变现策略

相对于普通投资者,大规模持有某种资产的机构投资者在交易这种资产时,其行为会导致资产价格的单向变动,从而产生流动性风险。针对机构投资者在连续时间框架且股票价格服从几何布朗运动的情况,提出在随机冲击下其完全变现行为的最优变现策略,利用最优控制理论中的极小值原理研究其最优变现策略。敏感性分析表明,最优变现策略由市场价格波动率、资产的流动性和机构投资者的风险厌恶偏好共同决定。以深发展股票为例,验证了机构投资者在随机冲击下可根据上述结论选择合适的最优变现策略,降低其在市场中所面临的流动性风险,使得股票的账面价值更可能多的转换为实际收益。     

The Impact of Short-Sale Constraints on Asset Allocation Strategies via the Backward Markov Chain Approximation Method

This paper considers an asset allocation strategy over a finite period under investment uncertainty and short-sale constraints as a continuous-time stochastic control problem. Investment uncertainty is characterised by a stochastic interest rate and inflation risk. If there are no short-sale constraints, the optimal asset allocation strategy can be obtained analytically. We consider several kinds of short-sale constraints and employ the backward Markov chain approximation method to explore the impact of short-sale constraints on asset allocation decisions. Our results show that the short-sale constraints do indeed have a significant impact on these decisions.     

Asset pricing with dynamic programming

The study of asset price characteristics of stochastic growth models such as the risk-free interest rate, equity premium, and the Sharpe-ratio has been limited by the lack of global and accurate methods to solve dynamic optimization models. In this paper, a stochastic version of a dynamic programming method with adaptive grid scheme is applied to compute the asset price characteristics of a stochastic growth model. The stochastic growth model is of the type as developed by [Brock and Mirman (1972), Journal of Economic Theory, 4, 479–513 and Brock (1979), Part I: The growth model (pp. 165–190). New York: Academic Press; The economies of information and uncertainty (pp. 165–192). Chicago: University of Chicago Press. (1982). It has become the baseline model in the stochastic dynamic general equilibrium literature. In a first step, in order to test our procedure, it is applied to this basic stochastic growth model for which the optimal consumption and asset prices can analytically be computed. Since, as shown, our method produces only negligible errors, as compared to the analytical solution, in a second step, we apply it to more elaborate stochastic growth models with adjustment costs and habit formation. In the latter model preferences are not time separable and past consumption acts as a constraint on current consumption. This model gives rise to an additional state variable. We here too apply our stochastic version of a dynamic programming method with adaptive grid scheme to compute the above mentioned asset price characteristics. We show that our method is very suitable to be used as solution technique for such models with more complicated decision structure.      

Optimal investment problem under non-extensive statistical mechanics

The optimal investment problem in which the asset price process is modeled by the non-extensive statistical mechanics is studied in this paper. By the methods of deterministic control and the dynamic programming, we obtain the optimal strategy with logarithmic utility function, power utility function and quadratic utility function, respectively. Moreover, the numerical results indicate that the optimal investment strategy is affected by the non-extensive parameter, the proportion invested in the risky asset decreases as the wealth increases under quadratic utility function, but it remains unchanged under power utility and logarithmic utility function.     

A multiple objective stochastic portfolio selection problem with random Beta

When selecting a portfolio, we need to consider, in general, the portfolio return and portfolio risk. Many risk measures have been used in portfolio selection problems as the Beta risk measure, introduced by the capital asset pricing model. Most of the existing research papers suppose that security's Beta has a deterministic value. Recently, many researchers argued that in selecting the optimal portfolio, securities’ Beta should be considered as an uncertain parameter. In this paper, we set up fundamentals to model the portfolio's Beta as a random variable and propose a multiple objective stochastic portfolio selection model with random Beta. To solve the proposed model, we apply a stochastic goal programming approach. A numerical example from the US stock exchange market is reported.     

Direct data-driven portfolio optimization with guaranteed shortfall probability

This paper proposes a novel methodology for optimal allocation of a portfolio of risky financial assets. Most existing methods that aim at compromising between portfolio performance (e.g., expected return) and its risk (e.g., volatility or shortfall probability) need some statistical model of the asset returns. This means that: (i) one needs to make rather strong assumptions on the market for eliciting a return distribution, and (ii) the parameters of this distribution need be somehow estimated, which is quite a critical aspect, since optimal portfolios will then depend on the way parameters are estimated. Here we propose instead a direct, data-driven, route to portfolio optimization that avoids both of the mentioned issues: the optimal portfolios are computed directly from historical data, by solving a sequence of convex optimization problems (typically, linear programs). Much more importantly, the resulting portfolios are theoretically backed by a guarantee that their expected shortfall is no larger than an a-priori assigned level. This result is here obtained assuming efficiency of the market, under no hypotheses on the shape of the joint distribution of the asset returns, which can remain unknown and need not be estimated.     

Real‐time waiting‐price trading interval in a heterogeneous options market: a Bernoulli distribution

Options pricing remains an open research question that is challenging for both theoreticians and practitioners. Unlike many classical binomial models that assume a “representative agent,” the model suggested herein considers two players who are heterogeneous with respect to their estimations of the distribution of the underlying asset price on expiration day, and with respect to their levels of willingness to make a transaction (eagerness level). A two‐player binomial model is developed to find the real‐time optimal option price in two stages. First, we determine a primary feasible pricing domain. We then find a narrower feasible domain, termed the “waiting‐price trading interval,” meaning the region within which the players may either wait for better offers (due to a change in market conditions or player beliefs), or make an immediate transaction. The suggested model is formulated by a nonlinear optimization problem and the optimal price is shown to be unique. We demonstrate that the counter player's eagerness level has a significant effect on the proposed optimal option price. Using empirical analysis, several known lattice‐based models for option pricing, such as CRR and Tian, are compared with the current model (herein, S‐H) in which the price offered by the model player takes into account the subjective beliefs of the opposing market player. The comparison shows significant advantages to the S‐H model in terms of the expected profit on expiration day.     

Impact of inflation on economic quantity discount schedules to increase vendor profits

In this paper we develop and analyse an inventory control vendor model in terms of an economic quantity discount (EQD) schedule under the effect of inflation. A multi item EQD model is proposed under several constraints such as floor soace and total number of orders. The optimal supply quantity and optimal discount schedule that the supplier can adopt under inflationary conditions is determined.     

Single-layer economic model predictive control for periodic operation

In this paper we consider periodic optimal operation of constrained periodic linear systems. We propose an economic model predictive controller based on a single layer that unites dynamic real time optimization and control. The proposed controller guarantees closed-loop convergence to the optimal periodic trajectory that minimizes the average operation cost for a given economic criterion. A priori calculation of the optimal trajectory is not required and if the economic cost function is changed, recursive feasibility and convergence to the new periodic optimal trajectory is guaranteed. The results are demonstrated with two simulation examples, a four tank system, and a simplified model of a section of Barcelona's water distribution network.