Robust risk-taking under a sustainable constraint

We consider a model in which the representative investor makes optimal portfolio and consumption choices robust to ambiguity with a sustainable constraint. We find that the influences of ambiguity on risk-taking are two ways. Those are gambling when the risk-free interest rate is less than a critical value, but derisk when the risk-free interest rate is greater than the critical value. Moreover, the erosion of ambiguity on consumption is more substantial in constrained cases, and ambiguity will magnify welfare losses.     

Trapezoidal approximations of fuzzy numbers preserving the expected interval — Algorithms and properties

Fuzzy number approximation by trapezoidal fuzzy numbers which preserves the expected interval is discussed. Algorithms for calculating the proper approximations are proposed and some properties of the approximation operators are discussed. It is shown that an adequate approximation operator might be chosen through the comparisons of some characteristics of the fuzzy number, like its ambiguity, width, its value and weighted expected value.     

A decision theory for partially consonant belief functions

Partially consonant belief functions (pcb), studied by Walley, are the only class of Dempster-Shafer belief functions that are consistent with the likelihood principle of statistics. Structurally, the set of foci of a pcb is partitioned into non-overlapping groups and within each group, foci are nested. The pcb class includes both probability function and Zadeh’s possibility function as special cases. This paper studies decision making under uncertainty described by pcb. We prove a representation theorem for preference relation over pcb lotteries to satisfy an axiomatic system that is similar in spirit to von Neumann and Morgenstern’s axioms of the linear utility theory. The closed-form expression of utility of a pcb lottery is a combination of linear utility for probabilistic lottery and two-component (binary) utility for possibilistic lottery. In our model, the uncertainty information, risk attitude and ambiguity attitude are separately represented. A tractable technique to extract ambiguity attitude from a decision maker behavior is also discussed.     

Reinsurance contract design when the insurer is ambiguity-averse

This paper investigates proportional and excess-loss reinsurance contracts in a continuous-time principal–agent framework, in which the insurer is the agent and the reinsurer is the principal. Insurance claims follow the classic Cramér–Lundberg process. The insurer believes that the claim intensity is uncertain and he chooses robust risk retention levels to maximize the penalty-dependent multiple-priors utility. The reinsurer designs reinsurance contracts subject to the insurer’s incentive compatibility constraints. The analytical expressions of the two robust reinsurance contracts are derived. Our results show that the robust reinsurance demand and price are greater than their respective standard values without model ambiguity, and increase as the insurer’s ambiguity aversion increases. Moreover, the reinsurer specifies a decreasing reinsurance price to induce increasing demand over time. Specifically, the price of excess-loss reinsurance is higher, relative to that of proportional reinsurance. Further, only if the insurer’s risk aversion is high or the reinsurer’s risk aversion is low, the insurer prefers the excess-loss reinsurance contract.     

An experimental study on matched field processing in shallow water

I.IntroductionPassiverangeanddepthlocalizationofanacousticsourceinshallowwaterisadifficult,yetinterestingproblemthathasreceivedagreatdealofattentioninthelastfewyears['5].Thesimu1taneousestimationofrangeanddepthrequirestheuseofnumericalpropagationmodels.Theclassicalapproachtothisproblemisto"match"thereceivedacousticdatawiththesoundfieldpredictedbythepropagationmodelforanumberofhypotheticalrange/depthsourcelocatiolls.Thistechniqueiscalledmatchedfieldprocessing.Itiscommonlyacceptedthatthewavepro…     

On constructing expert Betas for single-index model

The aim of this paper is to design flexible decision making models for portfolio selection including expert’s knowledge and imprecise preferences provided by financial analysts and investors, respectively.     

Integration of fuzzy linguistic information in language comprehension

To successfully understand a natural language utterance, a person must simultaneously consider information about its perceptual, syntactic, semantic, and pragmatic structure. At each of these levels of analysis, the linguistic information is continuously but systematically variable. It is argued that in order to cope with and, in fact, exploit this continuous information requires fuzzy propositional representations of linguistic knowledge. Such a fuzzy propositional theoretical framework is proposed and models of several specific language processing components are developed and empirically evaluated within this framework. The model system incorporates many of the major principles of current cognitive psychological theory and extends them into the fuzzy domain.     

Ambiguous chance constrained problems and robust optimization

In this paper we study ambiguous chance constrained problems where the distributions of the random parameters in the problem are themselves uncertain. We focus primarily on the special case where the uncertainty set of the distributions is of the form where ρ_p denotes the Prohorov metric. The ambiguous chance constrained problem is approximated by a robust sampled problem where each constraint is a robust constraint centered at a sample drawn according to the central measure The main contribution of this paper is to show that the robust sampled problem is a good approximation for the ambiguous chance constrained problem with a high probability. This result is established using the Strassen-Dudley Representation Theorem that states that when the distributions of two random variables are close in the Prohorov metric one can construct a coupling of the random variables such that the samples are close with a high probability. We also show that the robust sampled problem can be solved efficiently both in theory and in practice. Research partially supported by NSF grant CCR-00-09972. Research partially supported by NSF grants CCR-00-09972, DMS-01-04282, and ONR grant N000140310514.