Dynamic utility maximization with bounded shortfall risks

We address the dynamic portfolio optimization problem where the expected utility from terminal wealth has to be maximized. The special feature of this paper is an additional constraint on the portfolio strategy modeling bounded shortfall risks. We consider the risk, that the terminal wealth of the portfolio falls short of a certain benchmark. This benchmark is chosen to be proportional to the stock price. The risk is measured by the Expected Utility Loss. Using a continuous-time model of a complete financial market and applying martingale methods, analytic expressions for the optimal terminal wealth and the optimal portfolio strategies are given. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling attitudes towards uncertainty and risk through the use of choquet integral

The aim of this paper is to present in a unified framework a survey of some results related to Choquet Expected Utility (CEU) models, a promising class of models introduced separately by Quiggin [35], Yaari [48] and Schmeidler [40, 41] which allow to separate attitudes towards uncertainty (or risk) from attitudes towards wealth, while respecting the first order stochastic dominance axiom.     

Optimal portfolio with vector expected utility

We study the optimal portfolio selected by an investor who conforms to Siniscalchi (2009)’s Vector Expected Utility’s (VEU) axioms and who is ambiguity averse. To this end, we derive a mean–variance preference generalised to ambiguity from the second-order Taylor–Young expansion of the VEU certainty equivalent. We apply this Mean–Variance Variability preference to the static two-assets portfolio problem and deduce asset allocation results which extend the mean–variance analysis to ambiguity in the VEU framework. Our criterion has attractive features: it is axiomatically well-founded and analytically tractable, it is therefore well suited for applications to asset pricing as proved by a novel analysis of the home-bias puzzle with two ambiguous assets.     

House exchange and residential segregation in networks

This paper considers a Schelling model in an arbitrary fixed network where there are no vacant houses. Agents have preferences either for segregation or for mixed neighborhoods. Utility is non-transferable. Two agents exchange houses when the trade is mutually beneficial. We find that an allocation is stable when for two agents of opposite-color each black (white) agent has a higher proportion of neighbors who are black (white). This result holds irrespective of agents’ preferences. When all members of both groups prefer mixed neighborhoods, an allocation is also stable provided that if an agent belongs to the minority (majority), then any neighbor of opposite-color is in a smaller minority (larger majority).     

Expected Shortfall and optimal hedging payoff

By using variational techniques, we provide an optimal payoff written on a given random variable for hedging – in the sense of minimizing the Expected Shortfall at a given threshold – a payoff written on another random variable. In numerous financially relevant examples, our result leads to optimal payoffs in closed form. From a theoretical viewpoint, our result is also useful for providing bounds to the classical Expected Shortfall minimization problem with given financial instruments.     

Mean-risk analysis with enhanced behavioral content

We study a mean-risk model derived from a behavioral theory of Disappointment with multiple reference points. One distinguishing feature of the risk measure is that it is based on mutual deviations of outcomes, not deviations from a specific target. We prove necessary and sufficient conditions for strict first and second order stochastic dominance, and show that the model is, in addition, a Convex Risk Measure. The model allows for richer, and behaviorally more plausible, risk preference patterns than competing models with equal degrees of freedom, including Expected Utility (EU), Mean–Variance (M-V), Mean-Gini (M-G), and models based on non-additive probability weighting, such as Dual Theory (DT). In asset allocation, the model allows a decision-maker to abstain from diversifying in a positive expected value risky asset if its performance does not meet a certain threshold, and gradually invest beyond this threshold, which appears more acceptable than the extreme solutions provided by either EU and M-V (always diversify) or DT and M-G (always plunge). In asset trading, the model provides no-trade intervals, like DT and M-G, in some, but not all, situations. An illustrative application to portfolio selection is presented. The model can provide an improved criterion for mean-risk analysis by injecting a new level of behavioral realism and flexibility, while maintaining key normative properties.     

On a generalization of the Gerber-Shiu function to path-dependent penalties

The Expected Discounted Penalty Function (EDPF) was introduced in a series of now classical papers ( [Gerber and Shiu, 1997], [Gerber and Shiu, 1998a] and [Gerber and Shiu, 1998b]). Motivated by applications in option pricing and risk management, and inspired by recent developments in fluctuation theory for Lévy processes, we study an extended definition of the expected discounted penalty function that takes into account a new ruin-related random variable. In addition to the surplus before ruin and deficit at ruin, we extend the EDPF to include the surplus at the last minimum before ruin. We provide an expression for the generalized EDPF in terms of convolutions in a setting involving a subordinator and a spectrally negative Lévy process. Some expressions for the classical EDPF are recovered as special cases of the generalized EDPF.     

A multiscale time model with piecewise constant argument for a boundedly rational monopolist

We present a dynamic model for a boundedly rational monopolist who, in a partially known environment, follows a rule-of-thumb learning process. We assume that the production activity is continuously carried out and that the costly learning activity only occurs periodically at discrete time periods, so that the resulting dynamical model consists of a piecewise constant argument differential equation. Considering general demand, cost and agent’s reactivity functions, we show that the behavior of the differential model is governed by a nonlinear discrete difference equation. Differently from the classical model with smooth argument, unstable, complex dynamics can arise. The main novelty consists in showing that the occurrence of such dynamics is caused by the presence of multiple (discrete and continuous) time scales and depends on size of the time interval between two consecutive learning processes, in addition to the agent’s reactivity and the sensitivity of the marginal profit.     

风险规避和最优套期保值比率

在一般的期望效用框架下,研究投资者的风险厌恶态度对于其套期保值策略的影响.首先,给出了投资者采用不同套期保值策略时,效用函数应该满足的条件;其次,讨论了期望效用框架下,Rubinstein整体风险厌恶度量与经典的Arrow Pratt局部风险厌恶度量和更强的Ross的风险度量之间的关系,提出了一组条件,使得在该组条件下,风险厌恶的人际间比较可以用Rubinstein整体风险厌恶度量来刻画;最后,在现货和期货服从正态分布的假设下,使用之前提出的条件,研究投资者风险厌恶程度对于其持有的最优套期保值比率的影响.     

Portfolio theory for the recourse certainty equivalent maximizing investor

The portfolio selection problem with one safe andn risky assets is analyzed via a new decision theoretic criterion based on the Recourse Certainty Equivalent (RCE). Fundamental results in portfolio theory, previously studied under the Expected Utility criterion (EU), such as separation theorems, comparative static analysis, and threshold values for inclusion or exclusion of risky assets in the optimal portfolio, are obtained here. In contrast to the EU model, our results for the RCE maximizing investor do not impose restrictions on either the utility function or the underlying probability laws. We also derive a dual portfolio selection problem and provide it with a concrete economic interpretation.Research partly supported by ONR Contracts N0014-81-C-0236 and N00014-82-K-0295, and NSF Grant SES-8408134 with the Center for Cybernetic Studies, The University of Texas at Austin.Partly supported by NSF Grant DDM-8896112.Partly supported by AFOSR Grant 0218-88 and NSF Grant ECS-8802239 at the University of Maryland, Baltimore Campus.     

基于DNA遗传算法的随机整数规划期望值模型求解

为了求解随机整数规划问题,提出了随机整数规划期望值模型的概念,分析了利用DNA遗传算法求解此类问题的优点,并设计了求解算法,最后通过报童问题,验证了算法的可行性和有效性.     

Approximate representation of the de Sitter group

The purpose of this paper is to develop a theory of approximate representations of the de Sitter group considered as a perturbation of the Poincaré group. This approach simplifies investigation of relativistic effects pertaining to the mechanics in the de Sitter universe. Utility of the approximate approach is manifest if one compares the transformations of the de Sitter group with their approximate representations.     

Optimal insurance under rank-dependent expected utility

We re-visit the problem of optimal insurance design under Rank-Dependent Expected Utility (RDEU) examined by Bernard et al. (2015), Xu (2018), and Xu et al. (2018). Unlike the latter, we do not impose the no-sabotage condition on admissible indemnities, that is, that indemnity and retention functions be nondecreasing functions of the loss. Rather, in a departure from the aforementioned work, we impose a state-verification cost that the insurer can incur in order to verify the loss severity, hence automatically ruling out any ex post moral hazard that could otherwise arise from possible misreporting of the loss by the insured. We fully characterize the optimal indemnity schedule and discuss how our results relate to those of Bernard et al. (2015) and Xu et al. (2018). We then extend the setting by allowing for a distortion premium principle, with a distortion function that differs from that of the insured, and we provide a characterization of the optimal retention in that case.     

The existence of good Markov strategies for decision processes with general payoffs

For countable-state decision processes (dynamic programming problems), a general class of objective functions is identified for which it is shown that good Markov strategies always exist. This class includes product and lim inf rewards, as well as practically all the classical dynamic programming expected payoff functions.     

Recursiveness of indifference prices and translation-invariant preferences

We consider an economic agent with dynamic preferences over a set of uncertain monetary payoffs. We assume that preferences are updated in a time-consistent way as more information is becoming available. Our main result is that the agent’s indifference prices are recursive if and only if the preferences are translation-invariant. The proof is based on a characterization of time-consistency of dynamic preferences in terms of indifference sets. As a special case, we obtain that expected utility leads to recursive indifference prices if and only if absolute risk aversion is constant, that is, the Bernoulli utility function is linear or exponential.     

代理人在职消费对动态多任务激励契约的影响

将代理人的在职消费行为引入到动态多任务委托代理框架中,构造了代理人在职消费行为下的两阶段多任务模型,分析了代理人在职消费行为对动态多任务激励契约的影响.研究结果表明:一是任务为两阶段时,无论代理人有无在职消费行为,代理人的努力程度随着时间均呈上升趋势,这就表明当委托人在设计契约时,如果委托人期望代理人在第一阶段的努力水平不低于第二阶段的努力水平,就需要适当提高第一阶段的业绩薪酬系数;二是代理人在职消费自利行为并不一定会提高自身的努力程度,需要依据在职消费行为对绩效的影响情形来具体分析;三是在两阶段内,代理人存在在职消费时,委托人可适当降低业绩薪酬系数.     

一类随机图的演化

定义一随机图过程:如果图Gt-1不是完全图时,图Gt分别以概率p和q加一个点和一条有向边;如果图Gt-1是完全图时,则以概率1加一个点．研究图Gt顶点和边的概率分布以及当顶点数固定时,边数的期望界值估计．     

Inequity aversion in a joint economic lot sizing environment with asymmetric holding cost information

Screening contracts (or ‘menu of contracts’) are frequently used for aligning the incentives in supply chains with private information. In this context, it is assumed that all supply chain parties are strictly (expected) profit-maximizing. However, previous empirical work shows that this is a critical assumption. In fact, it seems that inequity adverse subjects are willing to invest money for achieving higher relative payoffs. Interestingly, the classical approach to design incentive compatible mechanisms gives the agent cheap leeway to increase relative pecuniary payoffs and thereby achieving more equitable profit allocations, because the agent is left (almost) indifferent between two contract alternatives. In other words, we argue (and actually observe in laboratory experiments) that this classical approach of contract design allows the agent to achieve more equitable outcomes at low cost. Since the agent’s better relative performance solely stems from reducing the principal’s payoffs, we observe a substantial negative impact on the overall supply chain performance. The present work relaxes the assumption of the profit-maximizing buyer (agent) in a serial supply chain for a lot sizing framework with asymmetrically distributed holding cost information and deterministic end-customer demand. The study provides researchers and managers an approach on how to account for disadvantageous inequity aversion (ie, the agent suffers from profits being lower than the principals profits) by designing a contract that anticipates such behaviour while providing a solution method for the resulting non-linear mathematical program. We denote the resulting contract as ‘behavioural robust’, since it limits the inefficiency losses that result if agents exhibit disadvantageous inequity aversion instead of being strictly profit-maximizing. A numerical study compares the advantages of the ‘behavioural robust’ contract against the classical screening contract. The results highlight that supply chain performance losses can be substantially reduced under the behavioural robust contract.     

Stochastic processes determined by a general success-breeds-success principle

The general “success-breeds-success” (SBS) principle as introduced in a previous paper extends the classical SBS principle in that the allocation of items over sources is determined by a more general rule than in the classical case. In this article we study the time evolution of the total number of sources, the average number of items per source and the number of sources with n items at time t, in the general SBS framework. Conditional as well as absolute expectations are calculated. Moreover, we investigate if and when these processes are martingales, supermartingales or submartingales. Stability results for the stochastic processes are obtained in the sense that we are able to determine when these processes converge. The article also studies the evolution of the expected average number of items per source.     

A multi-criteria large neighbourhood search for the transportation of disabled people

This paper addresses the problem of optimizing the transportation of disabled persons from home to specialized centres or schools. It is modelled as a Dial-a-ride problem (DARP), where several people share the same destination. Particular emphasis is placed on the objective function in order to consider several potentially conflicting interests. We propose a multi-criteria model from Multi-attribute Utility Theory based on the Choquet integral. The resulting multi-criteria DARP is then solved with a large neighbourhood search algorithm. This method includes classical destroy and repair heuristics as well as new operators exploiting the shared destination feature and criterion-specific operators. The algorithm is evaluated on a set of 14 real-world instances in the field of health care logistics, with up to 200 requests and 51 destination points.