Bayesian portfolio selection with multi-variate random variance models

We consider multi-period portfolio selection problems for a decision maker with a specified utility function when the variance of security returns is described by a discrete time stochastic model. The solution of these problems involves a dynamic programming formulation and backward induction. We present a simulation-based method to solve these problems adopting an approach which replaces the preposterior analysis by a surface fitting based optimization approach. We provide examples to illustrate the implementation of our approach.     

Multistage stochastic portfolio optimisation in deregulated electricity markets using linear decision rules

The deregulation of electricity markets increases the financial risk faced by retailers who procure electric energy on the spot market to meet their customers’ electricity demand. To hedge against this exposure, retailers often hold a portfolio of electricity derivative contracts. In this paper, we propose a multistage stochastic mean-variance optimisation model for the management of such a portfolio. To reduce computational complexity, we apply two approximations: we aggregate the decision stages and solve the resulting problem in linear decision rules (LDR). The LDR approach consists of restricting the set of recourse decisions to those affine in the history of the random parameters. When applied to mean-variance optimisation models, it leads to convex quadratic programs. Since their size grows typically only polynomially with the number of periods, they can be efficiently solved. Our numerical experiments illustrate the value of adaptivity inherent in the LDR method and its potential for enabling scalability to problems with many periods.     

技术不确定环境下新产品策略的设计应用

技术的动态发展和企业间的竞争对企业新产品策略有很大影响,直接决定新产品的引进周期。本文在产业技术动态变化的随机环境下构建随机动态规划模型,关注产业技术进步、投资成本和产品市场竞争等影响因素,探讨企业进行新产品引进的周期选择,对新产品引进的周期和质量决策进行方法设计和应用举例。利用随机动态规划模型得出新产品引进的最优时间周期,用算例分析技术进步和产品研发成本对企业引进周期策略的影响,采取策略迭代的方法进行求解,发现技术进步较快时企业的新产品引进步伐也较快,研发成本的提高使企业的新产品引入步伐降低。     

A stochastic programming model for asset liability management of a Finnish pension company

This paper describes a stochastic programming model that was developed for asset liability management of a Finnish pension insurance company. In many respects the model resembles those presented in the literature, but it has some unique features stemming from the statutory restrictions for Finnish pension insurance companies. Particular attention is paid to modeling the stochastic factors, numerical solution of the resulting optimization problem and evaluation of the solution. Out-of-sample tests clearly favor the strategies suggested by our model over static fixed-mix and dynamic portfolio insurance strategies. Financial support from the Foundation for the Helsinki School of Economics under grants number 9981114 and 9981117 for P. Hilli and M. Koivu is gratefully acknowledged. The work of T. Pennanen was supported by Finnish Academy under contract no. 3385     

Solving multistage asset investment problems by the sample average approximation method

The vast size of real world stochastic programming instances requires sampling to make them practically solvable. In this paper we extend the understanding of how sampling affects the solution quality of multistage stochastic programming problems. We present a new heuristic for determining good feasible solutions for a multistage decision problem. For power and log-utility functions we address the question of how tree structures, number of stages, number of outcomes and number of assets affect the solution quality. We also present a new method for evaluating the quality of first stage decisions.     

A dynamic stochastic programming model for international portfolio management

We develop a multi-stage stochastic programming model for international portfolio management in a dynamic setting. We model uncertainty in asset prices and exchange rates in terms of scenario trees that reflect the empirical distributions implied by market data. The model takes a holistic view of the problem. It considers portfolio rebalancing decisions over multiple periods in accordance with the contingencies of the scenario tree. The solution jointly determines capital allocations to international markets, the selection of assets within each market, and appropriate currency hedging levels. We investigate the performance of alternative hedging strategies through extensive numerical tests with real market data. We show that appropriate selection of currency forward contracts materially reduces risk in international portfolios. We further find that multi-stage models consistently outperform single-stage models. Our results demonstrate that the stochastic programming framework provides a flexible and effective decision support tool for international portfolio management.     

Capacity allocation for demand of different customer-product-combinations with cancellations, no-shows, and overbooking when there is a sequential delivery of service

We consider a problem where different classes of customers can book different types of services in advance and the service company has to respond immediately to the booking request confirming or rejecting it. Due to the possibility of cancellations before the day of service, or no-shows at the day of service, overbooking the given capacity is a viable decision. The objective of the service company is to maximize profit made of class-type specific revenues, refunds for cancellations or no-shows as well as the cost of overtime. For the calculation of the latter, information of the underlying appointment schedule is required. Throughout the paper we will relate the problem to capacity allocation in radiology services. Drawing upon ideas from revenue management, overbooking, and appointment scheduling we model the problem as a Markov decision process in discrete time which due to proper aggregation can be optimally solved with an iterative stochastic dynamic programming approach. In an experimental study we successfully apply the approach to a real world problem with data from the radiology department of a hospital. Furthermore, we compare the optimal policy to four heuristic policies, of whom one is currently in use. We can show that the optimal policy significantly improves the currently used policy and that a nested booking limit type policy closely approximates the optimal policy and is thus recommended for use in practice.     

Approximate dynamic programming for capacity allocation in the service industry

We consider a problem where different classes of customers can book different types of service in advance and the service company has to respond immediately to the booking request confirming or rejecting it. The objective of the service company is to maximize profit made of class-type specific revenues, refunds for cancellations or no-shows as well as cost of overtime. For the calculation of the latter, information on the underlying appointment schedule is required. In contrast to most models in the literature we assume that the service time of clients is stochastic and that clients might be unpunctual. Throughout the paper we will relate the problem to capacity allocation in radiology services. The problem is modeled as a continuous-time Markov decision process and solved using simulation-based approximate dynamic programming (ADP) combined with a discrete event simulation of the service period. We employ an adapted heuristic ADP algorithm from the literature and investigate on the benefits of applying ADP to this type of problem. First, we study a simplified problem with deterministic service times and punctual arrival of clients and compare the solution from the ADP algorithm to the optimal solution. We find that the heuristic ADP algorithm performs very well in terms of objective function value, solution time, and memory requirements. Second, we study the problem with stochastic service times and unpunctuality. It is then shown that the resulting policy constitutes a large improvement over an “optimal” policy that is deduced using restrictive, simplifying assumptions.     

Multisourcing suppliers selection in service outsourcing

Multisourcing suppliers selection in service outsourcing involves selecting a supplier portfolio with a reasonable number of suppliers and better performance to cover aspiration levels of criteria. It is a specific weighted matching problem with new challenges. This paper proposes a decision method for solving this problem. In the proposed method, different formats of preference information, including numerical values, interval numbers and linguistic variables, are used to express alternative ratings. The technique for order preference by similarity to ideal solution is extended to aggregate the three formats of preference information. A bi-objective 0–1 linear programming model using the aggregated information is built to select a desired supplier portfolio, in which the objectives of minimization of suppliers number and maximization of supplier performance are involved. To solve this model, we transform it into an equivalent, and then an exact multi-objective branch-and-bound algorithm is developed to obtain Pareto-optimal solutions. In addition, a real case of an insurance company is used to illustrate the applicability of the proposed method.     

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.     

Portfolio Optimization with Stochastic Volatilities and Constraints: An Application in High Dimension

In this paper we are interested in an investment problem with stochastic volatilities and portfolio constraints on amounts. We model the risky assets by jump diffusion processes and we consider an exponential utility function. The objective is to maximize the expected utility from the investor terminal wealth. The value function is known to be a viscosity solution of an integro-differential Hamilton-Jacobi-Bellman (HJB in short) equation which could not be solved when the risky assets number exceeds three. Thanks to an exponential transformation, we reduce the nonlinearity of the HJB equation to a semilinear equation. We prove the existence of a smooth solution to the latter equation and we state a verification theorem which relates this solution to the value function. We present an example that shows the importance of this reduction for numerical study of the optimal portfolio. We then compute the optimal strategy of investment by solving the associated optimization problem.     

A labeling method for dynamic driver-task assignment with uncertain task durations

The problem of assigning drivers to cover tasks with service time windows and uncertain task durations is formulated as a dynamic stochastic decision model. We develop an adaptive labeling solution procedure that can incorporate various practical constraints and work rules. Experiments are conducted to evaluate the procedure's performance and compare the stochastic and deterministic formulations.     

Smooth Solutions to Optimal Investment Models with Stochastic Volatilities and Portfolio Constraints

Abstract. This paper deals with an extension of Merton's optimal investment problem to a multidimensional model with stochastic volatility and portfolio constraints. The classical dynamic programming approach leads to a characterization of the value function as a viscosity solution of the highly nonlinear associated Bellman equation. A logarithmic transformation expresses the value function in terms of the solution to a semilinear parabolic equation with quadratic growth on the derivative term. Using a stochastic control representation and some approximations, we prove the existence of a smooth solution to this semilinear equation. An optimal portfolio is shown to exist, and is expressed in terms of the classical solution to this semilinear equation. This reduction is useful for studying numerical schemes for both the value function and the optimal portfolio. We illustrate our results with several examples of stochastic volatility models popular in the financial literature.     

An analytic framework to develop policies for testing, prevention, and treatment of two-stage contagious diseases

In this paper we consider healthcare policy issues for trading off resources in testing, prevention, and cure of two-stage contagious diseases. An individual that has contracted the two-stage contagious disease will initially show no symptoms of the disease but is capable of spreading it. If the initial stages are not detected which could lead to complications eventually, then symptoms start appearing in the latter stage when it would be necessary to perform expensive treatment. Under a constrained budget situation, policymakers are faced with the decision of how to allocate budget for prevention (via vaccinations), subsidizing treatment, and examination to detect the presence of initial stages of the contagious disease. These decisions need to be performed in each period of a given time horizon. To aid this decision-making exercise, we formulate a stochastic dynamic optimal control problem with feedback which can be modeled as a Markov decision process (MDP). However, solving the MDP is computationally intractable due to the large state space as the embedded stochastic network cannot be decomposed. Hence we propose an asymptotically optimal solution based on a fluid model of the dynamics in the stochastic network. We heuristically fine-tune the asymptotically optimal solution for the non-asymptotic case, and test it extensively for several numerical cases. In particular we investigate the effect of budget, length of planning horizon, type of disease, population size, and ratio of costs on the policy for budget allocation.     

Computational issues in a stochastic finite horizon one product recovery inventory model

Inderfurth [OR Spektrum 19 (1997) 111] and Simpson [Operations Research 26 (1978) 270] have shown how the optimal decision rules in a stochastic one product recovery system with equal leadtimes can be characterized. Using these results we provide in this paper a method for the exact computation of the parameters which determine the optimal periodic policy. Since exact computation is, especially in case of dynamic demands and returns, quite time consuming, we also provide two different approximations. One is based on an approximation of the value-function in the dynamic programming problem while the other approximation is based on a deterministic model. By means of numerical examples we compare our results and discuss the performance of the approximations.     

基于通货膨胀风险和Heston随机波动率下的最优资产配置

本文考虑了基于均值-方差准则下的连续时间投资组合选择问题。为了对冲市场中的利率风险和通货膨胀风险,假定市场上存在可供交易的零息名义债券和零息通货膨胀指数债券。另外,投资者还可以投资一个价格具有Heston随机波动率的风险资产。首先建立了基于均值-方差框架下的最优投资组合问题,然后将原问题进行转换,利用随机动态规划方法和对偶Lagrangian原理,获得了均值-方差准则下的有效投资策略以及有效前沿的解析表达形式,最后对相关参数的敏感性进行了分析。     

Optimal portfolio choice for an insurer with loss aversion

The problem of optimal investment for an insurance company attracts more attention in recent years. In general, the investment decision maker of the insurance company is assumed to be rational and risk averse. This is inconsistent with non fully rational decision-making way in the real world. In this paper we investigate an optimal portfolio selection problem for the insurer. The investment decision maker is assumed to be loss averse. The surplus process of the insurer is modeled by a Lévy process. The insurer aims to maximize the expected utility when terminal wealth exceeds his aspiration level. With the help of martingale method, we translate the dynamic maximization problem into an equivalent static optimization problem. By solving the static optimization problem, we derive explicit expressions of the optimal portfolio and the optimal wealth process.     

Smooth Solutions to Optimal Investment Models with Stochastic Volatilities and Portfolio Constraints

   Abstract. This paper deals with an extension of Merton's optimal investment problem to a multidimensional model with stochastic volatility and portfolio constraints. The classical dynamic programming approach leads to a characterization of the value function as a viscosity solution of the highly nonlinear associated Bellman equation. A logarithmic transformation expresses the value function in terms of the solution to a semilinear parabolic equation with quadratic growth on the derivative term. Using a stochastic control representation and some approximations, we prove the existence of a smooth solution to this semilinear equation. An optimal portfolio is shown to exist, and is expressed in terms of the classical solution to this semilinear equation. This reduction is useful for studying numerical schemes for both the value function and the optimal portfolio. We illustrate our results with several examples of stochastic volatility models popular in the financial literature.     

CEV模型下家庭最优投资决策问题

考虑固定收入下具有随机支出风险的家庭最优投资组合决策问题.在假设投资者拥有工资收入的同时将财富投资到一种风险资产和一种无风险资产,其中风险资产的价格服从CEV模型,无风险利率采用Vasicek随机利率模型.当支出过程是随机的且服从跳-扩散风险模型时,运用动态规划的思想建立了使家庭终端财富效用最大化的HJB方程,采用Legendre-对偶变换进行求解,得到最优策略的显示解,并通过敏感性分析进行验证表明,家庭投资需求是弹性方差系数的减函数,解释了家庭流动性财富的增加对最优投资比例呈现边际效用递减趋势.