二层次消费与投资决策优化动态规划模型

在动态多阶段情形,投资者面临的环境不仅只有投资环境,还包括消费环境.投资者关于投资与消费的决策具有层次性.因为消费事关人的生存需要,是优先要考虑的问题,且投资的最终目的还是为了消费,所以使消费最大化应是高一层次的目标,而使投资最大化则应是次一级的目标.因此,试图建立一个二层次消费与投资决策优化动态规划模型,以便更好地模拟现实世界的情况.讨论了该模型的动态决策过程和最优解的性质.     

Consumption/investment problem when the investment opportunity set can be enlarged by information gathering

I investigate an optimal information gathering and consumption/investment choice of an investor who can find a better opportunity by an information gathering option. I obtain a closed form solution, under which, the investor gathers information as soon as his wealth exceeds a certain critical level, consumes less and takes more risk than he would in the absence of such an option.     

Portfolio optimization for a large investor under partial information and price impact

This paper studies portfolio optimization problems in a market with partial information and price impact. We consider a large investor with an objective of expected utility maximization from terminal wealth. The drift of the underlying price process is modeled as a diffusion affected by a continuous-time Markov chain and the actions of the large investor. Using the stochastic filtering theory, we reduce the optimal control problem under partial information to the one with complete observation. For logarithmic and power utility cases we solve the utility maximization problem explicitly and we obtain optimal investment strategies in the feedback form. We compare the value functions to those for the case without price impact in Bäuerle and Rieder (IEEE Trans Autom Control 49(3):442–447, 2004) and Bäuerle and Rieder (J Appl Prob 362–378, 2005). It turns out that the investor would be better off due to the presence of a price impact both in complete-information and partial-information settings. Moreover, the presence of the price impact results in a shift, which depends on the distance to final time and on the state of the filter, on the optimal control strategy.     

通胀环境下股价波动率具有奈特不确定的最优消费与投资问题

本文在通胀环境和连续时间模型假设下,研究股票价格波动率具有奈特不确定对投资者的最优消费和投资策略的影响．首先在通胀环境和股票价格波动率具有奈特不确定的条件下,建立最优消费与投资问题的随机控制数学模型,得到了最优消费与投资所满足的HJB方程,并在常相对风险厌恶效用的情形下,获得最优化问题值函数的显式解．其次在通胀环境中当股价波动率具有奈特不确定时,得到了含糊厌恶的投资者是基于股价波动率的上界作出决策,并给出了投资者的最优投资和消费策略．最后在给定参数的条件下,对所得结果进行数值模拟和经济分析．     

What is the impact of stock market contagion on an investor’s portfolio choice?

Stocks are exposed to the risk of sudden downward jumps. Additionally, a crash in one stock (or index) can increase the risk of crashes in other stocks (or indices). Our paper explicitly takes this contagion risk into account and studies its impact on the portfolio decision of a CRRA investor both in complete and in incomplete market settings. We find that the investor significantly adjusts his portfolio when contagion is more likely to occur. Capturing the time dimension of contagion, i.e. the time span between jumps in two stocks or stock indices, is thus of first-order importance when analyzing portfolio decisions. Investors ignoring contagion completely or accounting for contagion while ignoring its time dimension suffer large and economically significant utility losses. These losses are larger in complete than in incomplete markets, and the investor might be better off if he does not trade derivatives. Furthermore, we emphasize that the risk of contagion has a crucial impact on investors’ security demands, since it reduces their ability to diversify their portfolios.     

Allocating costs of a shared server with stochastic service parameters and job class priorities

This paper develops an approach to allocate common costs to two divisions that share a process, where there is a trade-off between the joint investment in the process and the delays that a division’s jobs are expected to experience there. We allow one division’s jobs to have priority over the other division’s jobs. One purpose of allocation is to obtain accuracy in costing of products reflecting their consumption of resources. The second purpose, the incentive issue, is to elicit truthful reports of private information possessed by each division on (i) delay cost parameters or (ii) expected usage, this information being needed for the investment decision. In case (i), we find that when a division’s private information on its delay costs is poor or non-existent, it would prefer to invest at a weakly higher level than its accounting cost information justifies. In other words, a firm that allocates service center costs depending only on accounting measures of delay costs will under-invest in a shared facility. In case (ii), we find that to elicit truthful reporting by divisions requires a cost allocation rule that involves a complex monitoring of various physical parameters broadly related to the pattern of waiting times. This complexity is driven by the fact that one division has priority. However because actual usage provides an ex post estimate of expected usage up to some random error, a penalty scheme based on directly monitoring actual usage can be used to enforce truth telling up to any desired approximation.     

Fuzzy portfolio selection model with real features and different decision behaviors

In the ever changing financial markets, investor’s decision behaviors may change from time to time. In this paper, we consider the effect of investor’s different decision behaviors on portfolio selection in fuzzy environment. We present a possibilistic mean-semivariance model for fuzzy portfolio selection by considering some real investment features including proportional transaction cost, fixed transaction cost, cardinality constraint, investment threshold constraints, decision dependency constraints and minimum transaction lots. To describe investor’s different decision behaviors, we characterize the return rates on securities by LR fuzzy numbers with different shape parameters in the left- and right-hand reference functions. Then, we design a novel hybrid differential evolution algorithm to solve the proposed model. Finally, we provide a numerical example to illustrate the application of our model and the effectiveness of the designed algorithm.     

Non-separation in the mean–lower-partial-moment portfolio optimization problem

With a number of advantages, lower partial moments (LPM) serve as alternatives to variance as measures of portfolio risk. For two specific targets, a separation property holds in the context of mean–LPM portfolio optimization that allows investors to separate the decision about investment proportions among risky assets from the decision about how much to invest in risky versus risk-free assets. For other targets, however, separation is not guaranteed, and this case has not received much attention in the literature. We show in the case of non-separation that investment curves are not common to all optimizing investors, but that they are convex in (mean, LPM) space and their lower envelope is the efficient frontier. We consider the interesting behavior of investment curves and optimal risky portfolios. We also show empirically that an investor who mistakenly assumes separation holds will not experience significant excess portfolio risk in all practical cases.     

Bounds on the value of information in uncertain decision problems

The cost of obtaining good information regarding the various probability distributions needed for the solution of most stochastic decision problems is considerable. It is important to consider questions such as: (1) what minimal amounts of information are sufficient to determine optimal decision rules; (2) what is the value of obtaining knowledge of the actual realization of the random vectors; and (3) what is the value of obtaining some partial information regarding the actual realization of the random vectors. This paper is primarily concerned with questions two and three when the decision maker has an a priori knowledge of the joint distribution function of the random variables. Some remarks are made regarding results along the lines of question one. Mention is made of assumptions sufficient so that knowledge of means, or of means, variances, co-variances and n-moments are sufficient for the calculation of optimal decision rules. The analysis of the second question leads to the development of bounds on the value of perfect information. For multiperiod problems it is important to consider when the perfect information is available. Jensen's inequality is the key tool of the analysis. The calculation of the bounds requires the solution of nonlinear programs and the numerical evaluation of certain functions. Generally speaking, tighter bounds may be obtained only at the expense of additional information and computational complexity. Hence, one may wish to compute some simple bounds to decide upon the advisability of obtaining more information. For the analysis of the value of partial information it is convenient to introduce the notion of a signal. Each signal represents the receipt of certain information, and these signals are drawn from a given probability distribution. When a signal is received, it alters the decision maker's perception of the probability distributions inherent in his decision problem. The choice between different information structures must then take into account these probability distributions as well as the decision maker's preference function. A hierarchy of bounds may be determined for partial information evaluation utilizing the tools of the multiperiod perfect information case. However, the calculation of these bounds is generally considerably more dicult than the calculation of similar boulids in the perfect information case. Most of the analysis is directed towards problems in which the decision maker has a linear utility function over profits, costs or some other numerical variable. However, some of the bounds generalize to the case when the utility function is strictly increasing and concave.     

Families of relations modelling preferences under incomplete information

Let us consider a preferential information of type preference–indifference–incomparability (P, I, J), with additional information about differences in attractiveness between pairs of alternatives. The present paper offers a theoretical framework for the study of the “level of constraint” of this kind of partial preferential information. It suggests a number of structures as potential models being less demanding than the classical one in which differences in utilities can be used to represent the comparison of differences in attractiveness. The models are characterized in the more general context of families of non-complete preference structures, according to two different perspectives (called “semantico-numerical” and “matrix”). Both perspectives open the door to further practical applications connected with elicitation of the preferences of a decision maker.     

容许借贷的消费投资策略研究

考虑了容许借贷的消费投资决策问题,投资者选择债券和带有红利回报的风险股票,在效用最大化的标准下,研究了最优消费投资策略。最后就ＨＡＲＡ效用函数提供了最优策略。     

在线网络借贷投资决策模型及实证研究

P2P网络借贷作为电子商务在金融领域的延伸与应用,近年来得到广大学者的关注.但是目前的理论研究中,鲜有从投资者信息挖掘的角度进行投资决策分析.本文提出一个新颖的方法,即投资者构成分析方法,通过分析贷款的众多投资者信息遴选出最有价值的投资,辅助投资者进行投资决策.首先从投资者的历史投资收益率、风险偏好以及投资经验三个维度构建投资者档案(investor profile),进而基于投资者档案构建投资者构成分析模型,最后通过美国最大的在线网络借贷网站Prosper的数据,对本文提出的构想及模型进行了实证研究.实验结果表明本文提出的利用投资者构成分析的方法辅助投资者进行投资决策是可行的,文中构建的模型表现出良好的预测能力,能够有效地筛选出有价值的投资.     

基于回收期的科技创新项目决策模型分析

回收期方法是一种常用的评价方法.本文通过实物期权思想,对在不确定性下的科技创新项目,论证了回收期方法是合理的,通过本文的计算分析可知,较短的回收期隐含着较少的等待价值,也隐含着较高的单位资本回报.因此,利用回收期方法评价科技创新项目,不仅能得出与NPV方法评价的同样结论,而且还给投资者更多的信息,如几年之内可望收回投资.这对于资本不太雄厚的投资者来说更具有实际的意义,而对于资本雄厚的投资者也提供了能获得更多回报的投资决策评价方法.     

基于随机双曲折现的投资消费及效用无差别定价

在随机双曲折现条件下,显式地给出了具有指数函数(CARA)效用的最优跨期消费与投资组合;在非完备市场下,显式给出了基于CARA效用的收益流的效用无差别价格.结果表明:最优投资比例以及收益流的价值不受随机双曲折现因子的影响;在低折扣阶段,本文的最优消费水平高于Merton模型下的对应值,低折扣时期越短或高低折扣值相差越大,消费差距越明显.     

服务关系对供应链信息分享和信任决策的影响研究

由于信息不对称,供应商和制造商之间的信息分享和信任决策是供应链协调的关键。为了获得充足供给,制造商分享其私有需求信息,但同时存在欺骗动机;鉴于制造商的信息分享,供应商进行信任决策和产能投资。本文通过构建服务价值模型,分析了供应商与制造商之间的服务关系对信息分享和信任决策的影响。研究结果表明如果供应商的服务价值足够高,制造商会选择真实分享信息,此时供应商可以充分信任制造商的信息;如果服务价值低,制造商会采取放大需求信息的欺骗行为,此时供应商应怀疑制造商所分享信息的真实性。     

Likelihood ratio testing on partial multinormal data

A test procedure is developed for determining whether information contained in partial multinormal vectors is sufficient to significantly alter estimates of multivariate normal population parameters. The procedure uses the likelihood ratio and provides an a priori decision mechanism for the Hocking-Marx estimation scheme.     

Decision making under incomplete data using the imprecise Dirichlet model

The paper presents an efficient solution to decision problems where direct partial information on the distribution of the states of nature is available, either by observations of previous repetitions of the decision problem or by direct expert judgements.To process this information we use a recent generalization of Walley’s imprecise Dirichlet model, allowing us also to handle incomplete observations or imprecise judgements, including missing data. We derive efficient algorithms and discuss properties of the optimal solutions with respect to several criteria, including Gamma-maximinity and E-admissibility. In the case of precise data and pure actions the former surprisingly leads us to a frequency-based variant of the Hodges–Lehmann criterion, which was developed in classical decision theory as a compromise between Bayesian and minimax procedures.     

Optimal surrender strategies for equity-indexed annuity investors

An equity-indexed annuity (EIA) is a hybrid between a variable and a fixed annuity that allows the investor to participate in the stock market, and earn at least a minimum interest rate. The investor sacrifices some of the upside potential for the downside protection of the minimum guarantee. Because EIAs allow investors to participate in equity growth without the downside risk, their popularity has grown rapidly.An optimistic EIA owner might consider surrendering an EIA contract, paying a surrender charge, and investing the proceeds directly in the index to earn the full (versus reduced) index growth, while using a risk-free account for downside protection. Because of the popularity of these products, it is important for individuals and insurers to understand the optimal policyholder behavior.We consider an EIA investor who seeks the surrender strategy and post-surrender asset allocation strategy that maximizes the expected discounted utility of bequest. We formulate a variational inequality and a Hamilton-Jacobi-Bellman equation that govern the optimal surrender strategy and post-surrender asset allocation strategy, respectively. We examine the optimal strategies and how they are affected by the product features, model parameters, and mortality assumptions. We observe that in many cases, the “no-surrender” region is an interval (w_l,w_u); i.e., that there are two free boundaries. In these cases, the investor surrenders the EIA contract if the fund value becomes too high or too low. In other cases, there is only one free boundary; the lower (or upper) surrender threshold vanishes. In these cases, the investor holds the EIA, regardless of how low (or high) the fund value goes. For a special case, we prove a succinct and intuitive condition on the model parameters that dictates whether one or two free boundaries exist.     

State subsidy and moral hazard in corporate financing

This paper investigates the impact of state subsidy on the behavior of the entrepreneur under asymmetric information. Several authors formulated concerns about state intervention as it can aggravate moral hazard in corporate financing. In the seminal paper of Holmström and Tirole (Q J Econ 112(3):663–691, 1997) a two-player moral hazard model is presented with an entrepreneur initiating a risky scalable project and a private investor (e.g. bank or venture capitalist) providing outside financing. The novelty of our research is that this basic moral hazard model is extended to the case of positive externalities and to three players by introducing the state subsidizing the project. It is shown that in the optimum, state subsidy does not harm, but improves the incentives of the entrepreneur to make efforts for the success of the project; hence in effect state intervention reduces moral hazard. Consequently, state subsidy increases social welfare which is defined as the sum of private and public net benefits. Also, the exact form of the state subsidy (ex-ante/ex-post, conditional/unconditional, refundable/nonrefundable) is irrelevant in respect of the optimal size and the total welfare effect of the project. Moreover, in case of nonrefundable subsidies state does not crowd out private investors; but on the contrary, by providing additional capital it boosts private financing. These results are mainly due to the special mechanism imbedded in our model by which the private investor is able to transform even the badly designed state subsidies into a success fee which is optimal from the incentive point of view.     

The Optimal Interaction between a Hedge Fund Manager and Investor

ABSTRACT

This study explores hedge funds from the perspective of investors and the motivation behind their investments. We model a typical hedge fund contract between an investor and a manager, which includes the manager’s special reward scheme, i.e., partial ownership, incentives and early closure conditions. We present a continuous stochastic control problem for the manager’s wealth on a hedge fund comprising one risky asset and one riskless bond as a basis to calculate the investors’ wealth. Then we derive partial differential equations (PDEs) for each agent and numerically obtain the unique viscosity solution for these problems. Our model shows that the manager’s incentives are very high and therefore investors are not receiving profit compared to a riskless investment. We investigate a new type of hedge fund contract where the investor has the option to deposit additional money to the fund at half maturity time. Results show that investors’ inflow increases proportionally with the expected rate of return of the risky asset, but even in low rates of return, investors inflow money to keep the fund open. Finally, comparing the contracts with and without the option, we spot that investors are sometimes better off without the option to inflow money, thus creating a negative value of the option.