number of distinct sites visited by a random walker trapped by an absorbing boundary the number of distinct sites visited by a lattice random walker is a subject of continuing interest in both mathematics and physics all previous investigations have used the assumption that the lattice is unbounded an assessment of the amount of tissue interrogated by a photon in reflectance measurements for diagnostic purposes suggests analyzing properties of the average number of distinct sites visited by a random walker trapped by an absorbing plane at time t we show that for sufficiently large t this number is the same as the average number of distinct sites visited for this time when the surface is not present a more complete analysis is possible for a random walk on a line terminated by an absorbing point

mean first passage time of surface mediated diffusion in spherical domains we present an exact calculation of the mean first passage time to a target on the surface of a 2d or 3d spherical domain for a molecule alternating phases of surface diffusion on the domain boundary and phases of bulk diffusion the presented approach is based on an integral equation which can be solved analytically numerically validated approximation schemes which provide more tractable expressions of the mean first passage time are also proposed in the framework of this minimal model of surface mediated reactions we show analytically that the mean reaction time can be minimized as a function of the desorption rate from the surface

residence time distribution for a class of gaussian markov processes we study the distribution of residence time or equivalently that of mean magnetization for a family of gaussian markov processes indexed by a positive parameter alpha the persistence exponent for these processes is simply given by theta alpha but the residence time distribution is nontrivial the shape of this distribution undergoes a qualitative change as theta increases indicating a sharp change in the ergodic properties of the process we develop two alternate methods to calculate exactly but recursively the moments of the distribution for arbitrary alpha for some special values of alpha we obtain closed form expressions of the distribution function s1063 651x 99 03306 1

expected utility versus anticipated utility where do we stand abstract as is now widely admitted the expected utility hypothesis as a pattern of rational decision under risk or uncertainty is severely put into question many alternative models have been suggested which however may seem difficult to submit to comparative evaluations after giving a summary account of the issues involved the present paper aims at selecting among these models with the help of recent experimental evidence recent mathematical results and some epistemological arguments as a result the dichotomic models of decision under risk also called anticipated utility or rank dependent utility models independently designed by m allais j quiggin and m yaari appear as gathering strongest support

goal based portfolio choice model with discounted preference abstract this paper proposes goal based portfolio selection model with discounted preference firstly we discuss the goal based portfolio selection problem and then modify the portfolio selection model based on cumulative prospect theory cpt as well as considering investors discounted preference in psychology furthermore our proposed model is solved by martingale methods and an analytical solution with satisfying behavior is derived finally we select six different discounting functions to capture investors strategic changes numerical results show that investor with future bias performs adequate confidence and patience whereas investor with present bias tends to the immediate interests

dynamic decision making without expected utility an operational approach non expected utility theories such as rank dependent utility rdu theory have been proposed as alternative models to eu theory in decision making under risk these models do not share the separability property of expected utility theory this implies that in a decision tree if the reduction of compound lotteries assumption is made so that preferences at each decision node reduce to rdu preferences among lotteries and that preferences at different decision nodes are identical same utility function and same weighting function then the preferences are not dynamically consistent in particular the sophisticated strategy i e the strategy generated by a standard rolling back of the decision tree is likely to be dominated w r t stochastic dominance dynamic consistency of choices remains feasible and the decision maker can avoid dominated choices by adopting a non consequentialist behavior with his choices in a subtree possibly depending on what happens in the rest of the tree we propose a procedure which i although adopting a non consequentialist behavior involves a form of rolling back of the decision tree ii selects a non dominated strategy that realizes a compromise between the decision maker s discordant goals at the different decision nodes relative to the computations involved in the standard expected utility evaluation of a decision problem the main computational increase is due to the identification of non dominated strategies by linear programming a simulation using the rank dependent utility criterion confirms the computational tractability of the model

preference foundations for nonexpected utility a generalized and simplified technique this paper examines a tradeoff consistency technique for testing and axiomatically founding decision models the technique modifies earlier tradeoff consistency techniques by only considering indifferences not strict preferences the resulting foundations are both more general and more accessible than earlier results and they are so regarding both the technical and the intuitive axioms axiomatizations based on other bisymmetry like conditions also follow as corollaries from the results of this paper the tradeoff technique is applied to three popular theories of individual decision under uncertainty and risk i e expected utility choquet expected utility and prospect theory the conditions used are better suited for empirical measurements of utility than earlier tradeoff conditions and accordingly are easier to test

on the use of reverse brownian motion to accelerate hybrid simulations multiscale and multiphysics simulations are two rapidly developing fields of scientific computing efficient coupling of continuum deterministic or stochastic constitutive solvers with their discrete stochastic particle based counterparts is a common challenge in both kinds of simulations we focus on interfacial tightly coupled simulations of diffusion that combine continuum and particle based solvers the latter employs the reverse brownian motion rbm a monte carlo approach that allows one to enforce inhomogeneous dirichlet neumann or robin boundary conditions and is trivially parallelizable we discuss numerical approaches for improving the accuracy of rbm in the presence of inhomogeneous neumann boundary conditions and alternative strategies for coupling the rbm solver with its continuum counterpart numerical experiments are used to investigate the convergence stability and computational efficiency of the proposed hybrid algorithm

optimal investments for robust utility functionals in complete market models this paper introduces a systematic approach to the problem of maximizing the robust utility of the terminal wealth of an admissible strategy in a general complete market model where the robust utility functional is defined by a set q of probability measures our main result shows that this problem can often be reduced to determining a least favorable measure q0 q which is universal in the sense that it does not depend on the particular utility function the robust problem is thus equivalent to a standard utility maximization problem with respect to the subjective probability measure q0 by using the huber strassen theorem from robust statistics it is shown that q0 always exists if q is the i core of a 2 alternating capacity besides other examples we also discuss the problem of robust utility maximization with uncertain drift in a black scholes market and the case of weak information

risk ambiguity and the separation of utility and beliefs we introduce a general model of static choice under uncertainty arguably the weakest model achieving a separation of cardinal utility and a unique representation of beliefs most of the nonexpected utility models existing in the literature are special cases of it such separation is motivated by the view that tastes are constant whereas beliefs change with new information the model has a simple and natural axiomatization elsewhere forthcoming we show that it can be very helpful in the characterization of a notion of ambiguity aversion as separating utility and beliefs allows us to identify and remove aspects of risk attitude from the decision maker s behavior here we show that the model allows us to generalize several results on the characterization of risk aversion in betting behavior these generalizations are of independent interest as they show that some traditional results for subjective expected utility preferences can be formulated only in terms of binary acts

a parameter free elicitation of the probability weighting function in medical decision analysis an important reason why people violate expected utility theory is probability weighting previous studies on the probability weighting function typically assume a specific parametric form exclude heterogeneity in individual preferences and exclusively consider monetary decision making this study presents a method to elicit the probability weighting function in rank dependent expected utility theory that makes no prior assumptions about the functional form of the probability weighting function we use both aggregate and individual subject data thereby allowing for heterogeneity of individual preferences and we examine probability weighting in a new domain medical decision making there is significant evidence of probability weighting both at the aggregate and at the individual subject level the modal probability weighting function is inverse s shaped displaying both lower subadditivity and upper subadditivity probability weighting is in particular relevant at the boundaries of the unit interval compared to studies involving monetary outcomes we generally find more elevation of the probability weighting function the robustness of the empirical findings on probability weighting indicates its importance ignoring probability weighting in modeling decision under risk and in utility measurement is likely to lead to descriptively invalid theories and distorted elicitations

consistent modeling of risk averse behavior with spectral risk measures this paper introduces a new method for modeling risk averse behavior with spectral risk measures it is shown that recent approaches using phenomenological correspondences or results from robust statistics generally do not generate consistent results our method is based on the dual theory of choice we show that it is possible to encode preference relations in distorted probability measures which themselves induce admissible spectral risk measures this way risk averse behavior can be mapped onto the risk spectrum defining a spectral risk measure and can be quantified using a local pratt arrow like coecient

analytical representations of the spread harmonic measure density we study the spread harmonic measure that characterizes the spatial distribution of reaction events on a partially reactive surface for euclidean domains in which brownian motion can be split into independent lateral and transverse displacements we derive analytical formulas for the spread harmonic measure density and analyze its asymptotic behavior this analysis is applicable to slab domains general cylindrical domains and a half space we investigate the spreading effect due to multiple reflections on the surface and the underlying role of finite reactivity we discuss further extensions and applications of analytical results to describe laplacian transfer phenomena such as permeation through semipermeable membranes secondary current distribution on partially blocking electrodes and surface relaxation in nuclear magnetic resonance

certainty equivalents and information measures duality and extremal principles given a convex function ir ir the csiszar divergence csiszar 1978 is a function i ir n ir n ir

computation of convex bounds for present value functions with random payments in this contribution we study the distribution of the present value function of a series of random payments in a stochastic financial environment such distributions occur naturally in a wide range of applications within fields of insurance and finance we obtain accurate approximations by developing upper and lower bounds in the convex order sense for present value functions technically speaking our methodology is an extension of the results of dhaene et al insur math econom 31 1 2002 3 33 insur math econom 31 2 2002 133 161 to the case of scalar products of mutually independent random vectors

residence times and other functionals of reflected brownian motion we study the residence and local times for a brownian particle confined by reflecting boundaries and propose a general solution to the problem of finding the related probability distribution its fourier transform characteristic function and laplace transform survival probability are obtained in a compact matrix form involving the laplace operator eigenbasis explicit combinatorial relations are derived for the moments and the probability distribution is shown to be nearly gaussian when the exploration time is long enough when the eigenbasis or a part of it is known the numerical computation of the residence time distributions is straightforward and accurate the present approach can also be applied to investigate other functionals of reflected brownian motion describing in particular restricted diffusion in an external field or potential e g nuclei diffusing in an inhomogeneous magnetic field theoretical results for the local times are confronted with monte carlo simulations on the unit interval disk and sphere

fuzzy integral representation abstract in this paper we give representation results for nonlinear functionals in arbitrary spaces as fuzzy integrals the main assumption is that of comonotonic maxitivity i e i f g if ig for comonotonic f g under the more restrictive condition of stochastic dominance we prove a more specific representation as a fuzzy integral with respect to a distorted probability measure we discuss the particular cases of possibility measures and upper fuzzy expectations some partial randon nikodym results are proved for both the choquet and the fuzzy integrals finally an example is shown where the fuzzy integral representation is useful

great expectations part ii generalized expected utility as a universal decision rule many different rules for decision making have been introduced in the literature we show that a notion of generalized expected utility proposed in f chu j y halpern great expectation part i on the customizability of generalized expected utility in proc ijcai 03 acapulco mexico 2003 is a universal decision rule in the sense that it can essentially all other decision rules this approach gives us a general technique for designing new decision rules as well as providing a framework for comparing decision rules to each other

risk preferences on the space of quantile functions we propose a novel approach to quantification of risk preferences on the space of nondecreasing functions when applied to law invariant risk preferences among random variables it compares their quantile functions the axioms on quantile functions impose relations among comonotonic random variables we infer the existence of a numerical representation of the preference relation in the form of a quantile based measure of risk using conjugate duality theory by pairing the banach space of bounded functions with the space of finitely additive measures on a suitable algebra varsigma we develop a variational representation of the quantile based measures of risk furthermore we introduce a notion of risk aversion based on quantile functions which enables us to derive an analogue of kusuoka representation of coherent law invariant measures of risk

inverse stochastic dominance constraints and rank dependent expected utility theory we consider optimization problems with second order stochastic dominance constraints formulated as a relation of lorenz curves we characterize the relation in terms of rank dependent utility functions which generalize yaari s utility functions we develop optimality conditions and duality theory for problems with lorenz dominance constraints we prove that lagrange multipliers associated with these constraints can be identified with rank dependent utility functions the problem is numerically tractable in the case of discrete distributions with equally probable realizations

incremental elicitation of choquet capacities for multicriteria choice ranking and sorting problems this paper proposes incremental preference elicitation methods for multicriteria decision making with a choquet integral the choquet integral is an evaluation function that performs a weighted aggregation of criterion values using a capacity function assigning a weight to any coalition of criteria thus enabling positive and or negative interactions among them and covering an important range of possible decision behaviors however the specification of the capacity involves many parameters which raises challenging questions both in terms of elicitation burden and guarantee on the quality of the final recommendation in this paper we investigate the incremental elicitation of the capacity through a sequence of preference queries questions selected one by one using a minimax regret strategy so as to progressively reduce the set of possible capacities until the regret the worst case loss due to reasoning with only partially specified capacities is low enough we propose a new approach designed to efficiently compute minimax regret for the choquet model and we show how this approach can be used in different settings 1 the problem of recommending a single alternative 2 the problem of ranking alternatives from best to worst and 3 sorting several alternatives into ordered categories numerical experiments are provided to demonstrate the practical efficiency of our approach for each of these situations

collision statistics for random flights with anisotropic scattering and absorption for a broad class of random walks with anisotropic scattering kernels and absorption we derive explicit formulas that allow expressing the moments of the collision number n v performed in a volume v as a function of the particle equilibrium distribution our results apply to arbitrary domains v and boundary conditions and allow assessing the hitting statistics for systems where the typical displacements are comparable to the domain size so that the diffusion limit is possibly not attained an example is discussed for one dimensional random flights with exponential displacements where analytical calculations can be carried out

first exit times and residence times for discrete random walks on finite lattices in this paper we derive explicit formulas for the surface averaged first exit time of a discrete random walk on a finite lattice we consider a wide class of random walks and lattices including random walks in a nontrivial potential landscape we also compute quantities of interest for modeling surface reactions and other dynamic processes such as the residence time in a subvolume the joint residence time of several particles and the number of hits on a reflecting surface

the probability weighting function a probability weighting finction w p is a prominent feature of several non expected utility theories including prospect theoiy and rank dependent models empirical esti mates indicate that w p is regressive first w p p then iv p p s shaped first concave then convex and asymmetrical intersecting the diagonal at about 1 3 the paper states axioms for several w p forms including the compound invariant w p exp ln p 1 0 a 1 which is regressive s shaped and with an invariant fixed point and inflection point at i e 37 the common ratio effect allais 1953 refers to the obselvation that the more risky of two simple prospects becomes relatively more attractive when the probability of winning is reduced by equal proportion in both prospects thus a person who prefers a sure gain of 100 000 over a coin toss for 300 000 or nothing might also prefer a one in a million lottery ticket for 300 000 over a two in a million lottery ticket for 100 000 this contradicts expected utility but not common sense there is a world of difference between certainty and a 50 50 shot the difference between one or two chances in a million is negligible the example has all the force and simplicity of classical arguments for nonlinear utility where the utility interval from say 10 and 20 is taken as self evidently greater than the utility interval from 1 000 010 and 1 000 020 both arguments appeal directly to our intuitions about numbers a major point of difference is that the money argument involves a constant money intelval and the probability argument a constant probability ratio a minor difference is that in the money domain a constant interval has less impact as the numbers get larger while in the probability domain a constant ratio has less impact as the numbers get smaller putting the two demonstrations side by side like this raises an interesting question namely whether an account of nonlinearity in probabilities can be somehow adapted from classical utility theory modulo a log transformation converting statements about probability ratios into statements about utility intervals indeed in their seminal paper on prospect theory kahneman and tversky 1979 explained the common ratio effect by means of a nonlinear transformation of probabilities into decision weights p w p with log w

the dual theory of choice under risk in this essay a new theory of choice under risk is being proposed it is a theory which in a sense that will become clear is dual to expected utility theory hence the title dual theory risky prospects are evaluated in this theory by a cardinal numerical scale which resembles an expected utility except that the roles of payments and probabilities are reversed this theme the reversal of the roles of probabilities and payments will recur throughout the paper i should emphasize that playing games with probabilities masquerading as payments and payments masquerading as probabilities is not my object rather i hope to convince the reader that the dual theory has intrinsic economic significance and that in some areas its predictions are superior to those of expected utility theory while in other areas the reverse will be the case two reasons have prompted me to look for an alternative to expected utility theory the first reason is methodological in expected utility theory the agent s attitude towards risk and the agent s attitude towards wealth are forever bonded together at the level of fundamental principles risk aversion and diminishing marginal utility of wealth which are synonymous under expected utility theory are horses of different colors the former expresses an attitute towards risk increased uncertainty hurts while the latter expresses an attitude towards wealth the loss of a sheep hurts more when the agent is poor than when the agent is rich a question arises therefore as to whether these two notions can be kept separate from each other in a full fledged theory of cardinal utility the dual theory will have this property the second reason that leads me to look for an alternative to expected utility theory is empirical behavior patterns which are systematic yet inconsistent with expected utility theory have often been observed two prominent references among many others are allais 1953 and kahneman tversky 1979 so deeply

what common ground exists for descriptive prescriptive and normative utility theories descriptive and normative modeling of decision making under risk and uncertainty have grown apart over the past decade psychological models attempt to accommodate the numerous violations of rationality axioms including independence and transitivity meanwhile normatively oriented decision analysts continue to insist on the applied usefulness of the subjective expected utility seu model as this gap has widened two facts have remained largely unobserved first most people in real situations attempt to behave in accord with the most basic rationality principles even though they are likely to fail in more complex situations second the seu model is likely to provide consistent and rational answers to decision problems within a given problem structure but may not be invariant across structures thus people may be more rational than the psychological literature gives them credit for and applications of the seu model may be susceptible to some violations of invariance principles this paper attempts

stochastic comparisons of residual lifetimes and inactivity times of coherent systems with dependent identically distributed components abstract in this paper we compare the residual lifetime of a used coherent system of age t 0 with the lifetime of the similar coherent system made up of used components of age t here similar means that the system has the same structure and the component lifetimes have the same dependence joint reliability copula some comparison results are obtained for the likelihood ratio order failure rate order reversed failure rate order and the usual stochastic order similar results are reported for comparing inactivity time of a coherent system with lifetime of similar coherent system having component lifetimes same as inactivity times of failed components

canonical fuzzy measure on 0 1 abstract the fuzzy measure g on the unit interval 0 1 is called canonical if g is a distortion of the lebesgue measure the characterization of the canonical fuzzy measure is given by the invariance properties against translations

risk aversion in cumulative prospect theory this paper characterizes the conditions for strong risk aversion and second order stochastic dominance for cumulative prospect theory strong risk aversion implies a convex weighting function for gains and a concave one for losses it does not necessarily imply a concave utility function the latter does follow if the weighting functions are continuous by investigating the exact relationship between loss aversion and strong risk aversion a natural index for the degree of loss aversion is derived

mathematical basis for a general theory of laplacian transport towards irregular interfaces the theory of laplacian transport towards and across irregular surfaces is reformulated in terms of the dirichlet to neumann operator and its spectral characteristics this permits us to obtain an exact equivalent circuit for the impedance of a working interface of arbitrary shape the important result is that only very few eigenmodes of this operator do govern the entire response of a macroscopic system this property drastically simplifies the understanding of irregular or prefractal interfaces the results can be applied in electrochemistry physiology and chemical engineering fields where exchange processes across surfaces with complex geometry are ubiquitous

a behavioral foundation for fuzzy measures in savage 41 a behavioral foundation was given for subjective probabilities to be used in the maximization of expected utility this paper analogously gives a behavioral foundation for fuzzy measures to be used in the maximization of choquet expected utility this opens the way to empirical verification or falsification of fuzzy measures and frees them of their ad hoc character

probability weighting and l moments abstract several popular generalizations of expected utility theory cumulative prospect theory rank dependent utility and yaari s dual model allow for non linear transformation of de cumulative probabilities this paper shows an unexpected connection between probability weighting and the statistical theory of l moments specifically cubic probability weighting results in a linear tradeoff between the expected value the first l moment gini 1912 mean difference statistic the second l moment also known as l scale and the third l moment measuring skewness inverse s shaped probability weighting function crossing the 45 line at a probability 0 5 reflects an aversion to the dispersion of outcomes and an attraction to positively skewed distributions

residence time statistics for normal and fractional diffusion in a force field we investigate statistics of occupation times for an over damped brownian particle in an external force field using a backward fokker planck equation introduced by majumdar and comtet for an arbitrary potential field the distribution of occupation times is expressed in terms of solutions of the corresponding first passage time problem this general relationship between occupation times and first passage times is valid for normal markovian diffusion and for non markovian sub diffusion the latter modeled using the fractional fokker planck equation for binding potential fields we find in the long time limit ergodic behavior for normal diffusion while for the fractional framework weak ergodicity breaking is found in agreement with previous results of bel and barkai on the continuous time random walk on a lattice for non binding cases rich physical behaviors are obtained and classification of occupation time statistics is made possible according to whether or not the underlying random walk is recurrent and the averaged first return time to the origin is finite our work establishes a link between fractional calculus and ergodicity breaking

risk forms representation disintegration and application to partially observable two stage systems we introduce the concept of a risk form which is a real functional of two arguments a measurable function on a polish space and a measure on that space we generalize the duality theory and the kusuoka representation to this setting for a risk form acting on a product of polish spaces we define marginal and conditional forms and we prove a disintegration formula which represents a risk form as a composition of its marginal and conditional forms we apply the proposed approach to two stage stochastic programming problems with partial information and decision dependent observation distribution

counting statistics a feynman kac perspective by building upon a feynman kac formalism we assess the distribution of the number of collisions in a given region for a broad class of discrete time random walks in absorbing and nonabsorbing media we derive the evolution equation for the generating function of the number of collisions and we complete our analysis by examining the moments of the distribution and their relation to the walker equilibrium density some significant applications are discussed in detail in particular we revisit the gambler s ruin problem and generalize to random walks with absorption the arcsine law for the number of collisions on the half line

decomposition and characterization of risk with a continuum of random variables the paper studies the representation and characterization of risks generated by a continuum of random variables the main theorem is a characterization of a broad class of continuum processes in terms of the decomposition of risk into aggregate and idiosyncratic components and in terms of the approximation of the continuum process by finite collections of random variables this characterization is used to study decision making problems with anonymous and state independent payoffs an extension theorem shows that if such a payoff function is defined on simple processes then it has a unique continuous extension to the class of processes characterized in this paper this extension is formulated without reference to sample realizations and with minimal restrictions on the patterns of correlation between the random variables as an application the theory is used to develop a new model of large games which emphasizes the explicit description of the players randomizations this model is used to study the class of environments in which schmeidler s 1973 representation of strategic uncertainty in large games is valid

descriptive parameter for photon trajectories in a turbid medium in many applications of laser techniques for diagnostic or therapeutic purposes it is necessary to be able to characterize photon trajectories to know which parts of the tissue are being interrogated in this paper we consider the cw reflectance experiment on a semi infinite medium with uniform optical parameters and having a planar interface the analysis is carried out in terms of a continuous time random walk and the relation between the occupancy of a plane parallel to the surface to the maximum depth reached by the random walker is studied the first moment of the ratio of average depth to the average maximum depth yields information about the volume of tissue interrogated as well as giving some indication of the region of tissue that gets the most light we have also calculated the standard deviation of this random variable it is not large enough to qualitatively affect information contained in the first moment

choquet based optimisation in multiobjective shortest path and spanning tree problems this paper is devoted to the search of choquet optimal solutions in finite graph problems with multiple objectives the choquet integral is one of the most sophisticated preference models used in decision theory for aggregating preferences on multiple objectives we first present a condition on preferences name hereafter preference for interior points that characterizes preferences favouring compromise solutions a natural attitude in various contexts such as multicriteria optimisation robust optimisation and optimisation with multiple agents within choquet expected utility theory this condition amounts to using a submodular capacity and a convex utility function under these assumptions we focus on the fast determination of choquet optimal paths and spanning trees after investigating the complexity of these problems we introduce a lower bound for the choquet integral computable in polynomial time then we propose different algorithms using this bound either based on a controlled enumeration of solutions ranking approach or an implicit enumeration scheme branch and bound finally we provide numerical experiments that show the actual efficiency of the algorithms on multiple instances of different sizes

from fuzzy set theory to non additive probabilities how have economists reacted abstract in this paper we are going to try to conduct a comparative review of the two programmes devoted to the application of fuzzy sets theory in economics for the first and to nonadditive probabilities for the second while putting forward some explanations and conjecture as to their development and their future in section 1 we defend the thesis which claims that the first programme has only had a global focus on the approach in terms of generalization and we shall go deeper into the analysis of the particular area of general equilibrium as it is the programme on which ponsard worked the most in section 2 we shall seek to show that the second programme devoted to the introduction of nonadditive probabilities in decision theory on the contrary has attempted to come up with independent findings this would explain why this last programme has managed to fit into topics at a standstill or in crisis easily which is undeniably the case of the standard theory of decision making while the first programme was only envisaged as a kind of mathematical game involving the application of new rules to an old model in the case of the first programme one might thus speak of an extension principle and in the second case of a resolution principle

temporal resolution of uncertainty and recursive non expected utility models if an agent weakly prefers early resolution of uncertainty then the recursive forms of both the most commonly used non expected utility models betweenness and rank dependence almost reduce to kreps porteus s 1978 recursive expected utility

are people bayesian uncovering behavioral strategies abstract economists and psychologists have recently been developing new theories of decision making under uncertainty that can accommodate the observed violations of standard statistical decision theoretic axioms by experimental subjects we propose a procedure that finds a collection of decision rules that best explain the behavior of experimental subjects the procedure is a combination of maximum likelihood estimation of the rules together with an implicit classification of subjects to the various rules and a penalty for having too many rules we apply our procedure to data on probabilistic updating by subjects in four different universities we get remarkably robust results showing that the most important rules used by the subjects in order of importance are bayes s rule a representativeness rule ignoring the prior and to a lesser extent conservatism overweighting the prior

optimization with stochastic preferences based on a general class of scalarization functions it is of crucial importance to develop risk averse models for multicriteria decision making under uncertainty a major stream of the related literature studies optimization problems that feature multivariate stochastic benchmarking constraints these problems typically involve a univariate stochastic preference relation often based on stochastic dominance or a coherent risk measure such as conditional value at risk which is then extended to allow the comparison of random vectors by the use of a family of scalarization functions all scalarized versions of the vector of the uncertain outcomes of a decision are required to be preferable to the corresponding scalarizations of the benchmark outcomes while this line of research has been dedicated almost entirely to linear scalarizations the corresponding deterministic literature uses a wide variety of scalarization functions that among other advantages offer a high degree of modeling flexibility in this paper we aim to incorporate these scalarizations i

a genuine rank dependent generalization of the von neumann morgenstern expected utility theorem this paper uses revealed probability trade offs to provide a natural foundation for probability weighting in the famous von neumann and morgenstern axiomatic set up for expected utility in particular it shows that a rank dependent preference functional is obtained in this set up when the independence axiom is weakened to stochastic dominance and a probability trade off consistency condition in contrast with the existing axiomatizations of rank dependent utility the resulting axioms allow for complete flexibility regarding the outcome space consequently a parameter free test elicitation of rank dependent utility becomes possible the probability oriented approach of this paper also provides theoretical foundations for probabilistic attitudes towards risk it is shown that the preference conditions that characterize the shape of the probability weighting function can be derived from simple probability trade off conditions

fractional feynman kac equation for weak ergodicity breaking the continuous time random walk ctrw is a model of anomalous subdiffusion in which particles are immobilized for random times between successive jumps a power law distribution of the waiting times 1 leads to subdiffusion x 2 t for 0 1 in closed systems the long stagnation periods cause time averages to divert from the corresponding ensemble averages which is a manifestation of weak ergodicity breaking the time average of a general observable u t 1 t 0 t u x d is a functional of the path and is described by the well known feynman kac equation if the motion is brownian here we derive forward and backward fractional feynman kac equations for functionals of ctrw in a binding potential we use our equations to study two specific time averages the fraction of time spent by a particle in half box and the time average of the particle s position in a harmonic field in both cases we obtain the probability density function of the time averages for t and the first two moments our results show that both the occupation fraction and the time averaged position are random variables even for long times except for 1 when they are identical to their ensemble averages using our fractional feynman kac equation we also study the dynamics leading to weak ergodicity breaking namely the convergence of the fluctuations to their asymptotic values

fuzzy sets spl minus a convenient fiction for modeling vagueness and possibility this paper is a reply to laviolette and seaman s critical discussion of fuzzy set theory rather than questioning the interest of the bayesian approach to uncertainty some reasons why bayesian find the idea of a fuzzy set not palatable are laid bare some links between fuzzy sets and probability that laviolette and seaman seem not to be aware of are pointed out these links suggest that contrary to the claim sometimes found in the literature probability theory is not a special case of fuzzy set theory the major objection to laviolette and seaman is that they found their critique on as very limited view of fuzzy sets including debatable papers while they fail to account for significant works pertaining to axiomatic derivation of fuzzy set connectives possibility theory fuzzy random variables among others

the binomial decomposition of generalized gini welfare functions the s gini and lorenzen cases abstract we consider the binomial decomposition of generalized gini welfare functions in terms of the binomial welfare functions and the associated binomial inequality indices we examine in detail the weights of the binomial welfare functions and the coefficients of the associated binomial inequality indices which progressively focus on the poorest sector of the population and we illustrate the numerical behavior of the binomial welfare functions and inequality indices in relation with a new parametric family of income distributions the main contribution of the paper is to investigate the analogy between the binomial welfare functions and the s gini and lorenzen parametric families of generalized gini welfare functions particularly in the context of the binomial decomposition finally we examine the orness of the parametric s gini and lorenzen families of generalized gini welfare functions

first passage times for random walks in bounded domains we present a novel computational method of first passage times between a starting site and a target site of regular bounded lattices we derive accurate expressions for all the moments of this first passage time validated by numerical simulations their range of validity is discussed we also consider the case of a starting site and two targets in addition we present the extension to continuous brownian motion these results are of great relevance to any system involving diffusion in confined media

generalized evaluation in decision analysis the paper presents a discussion on evaluation methods in decision analysis the presentation begins with the discussion of the expected value rule for selection amongst a number of available courses of action then a number of other evaluation rules to either replace or supplement the expected value are presented they are discussed from a choice rather than preference view to improve the expected value rule or any other similar rule it is suggested that it should be supplemented with other qualitative rules rather than engaging in further modifications in pursuit of the perfect rule a characteristic of qualitative rules is that they do not rely on multiplying probabilities and values but treat them as separate numeric entities once a rule has been agreed upon it can be applied to all the alternatives provided there is a computational procedure for evaluating the alternatives under that rule delta dominance is introduced as a unifying concept for many of the dominance rules in current use dominance and threshold methods are discussed and the kinship between them is pointed out

comonotonicity and choquet integrals of hermitian operators and their applications in a quantum system with d dimensional hilbert space the q function of a hermitian positive semidefinite operator is defined in terms of the d 2 coherent states in this system the choquet integral of the q function of is introduced using a ranking of the values of the q function and mobius transforms which remove the overlaps between coherent states it is a figure of merit of the quantum properties of hermitian operators and it provides upper and lower bounds to various physical quantities in terms of the q function comonotonicity is an important concept in the formalism which is used to formalize the vague concept of physically similar operators comonotonic operators are shown to be bounded with respect to an order based on choquet integrals applications of the formalism to the study of the ground state of a physical system are discussed bounds for partition functions are also derived

higher order symmetrization inequalities and applications abstract we prove new extended forms of the polya szego symmetrization principle as a consequence new sharp embedding theorems for generalized sobolev and besov spaces are proved

calibration results for non expected utility theories rabin 2000 proved that a low level of risk aversion with respect to small gambles leads to a high and absurd level of risk aversion with respect to large gambles rabin s arguments strongly depend on expected utility theory but we show that similar arguments apply to general non expected utility theories

modeling attitude to risk in human decision processes an application of fuzzy measures abstract several models of the human decision process have been proposed classical examples of which are utility theory and prospect theory in recent times the theory of fuzzy measures and integrals has emerged as an alternative meriting further investigation specifically one is interested in the degrees of disjunction and conjunction and the veto and favor indices that represent the tolerance measure of the decision maker though several theoretical expositions have appeared in contemporary literature empirical studies applying these concepts to the real world are scarce this paper reports two studies based on a model of strategic telecommunication investment decisions from a research work involving a survey of executives the first study involves building fuzzy models corresponding to each individual decision maker with the results grouped based on the decision makers propensity to risk as determined by their degrees of disjunction the shapley indices and the interaction effects are determined for each pooled dataset corresponding to each group to contrast this approach with those of conventional nomothetic comparisons of decision policies the decision makers are grouped based on a clustering analysis of the individual linear regression models the data for each cluster are pooled and the fuzzy measures learned from the dataset are analyzed for comparison purposes the results not only serve as a demonstration of fuzzy measure analysis as a viable approach to studying qualitative decision making but also provide useful methodological insights into applying fuzzy measures to strategic investment decisions under risk

mixture symmetry and quadratic utility the independence axiom of expected utility theory has recently been weakened to the betweenness axiom in this paper an even weaker axiom called mixture symmetry is presented the corresponding functional structure is such that utility is a betweenness functional on part of its domain and quadratic in probabilities elsewhere the experimental evidence against betweenness provides one motivation for the more general theory presented here another advantage of the mixture symmetric class of utility functions is that it is sufficiently flexible to permit the disentangling of attitudes towards risk and towards randomization

branching exponential flights travelled lengths and collision statistics the evolution of several physical and biological systems ranging from neutron transport in multiplying media to epidemics or population dynamics can be described in terms of branching exponential flights a stochastic process which couples a galton watson birth death mechanism with random spatial displacements within this context one is often called to assess the length lv that the process travels in a given region v of the phase space or the number of visits nv to this same region in this paper we address this issue by resorting to the feynman kac formalism which allows characterizing the full distribution of lv and nv and in particular deriving explicit moment formulas some other significant physical observables associated to lv and nv such as the survival probability are discussed as well and results are illustrated by revisiting the classical example of the rod model in nuclear reactor physics

equilibrium routing under uncertainty we provide a brief introduction to the basic models used to describe traffic on congested networks both in urban transport and telecommunications we discuss traffic equilibrium models covering atomic and non atomic routing games with emphasis on situations where the travel times are subject to random fluctuations we use convex optimization to present the models in a unified framework that stresses the common underlying structures as a prototypical example of traffic equilibrium with elastic demands we discuss some models for routing and congestion control in telecommunications we also describe a class of stochastic dynamics that model the adaptive behavior of agents and which provides a plausible micro foundation for the equilibrium finally we present some recent ideas on how risk averse behavior might be incorporated in the equilibrium models

additivizations of nonadditive measures the concept of an additivization of a nonadditive probability measure is introduced and studied the relation to cooperative game theory is explored and it is shown that in many cases of interest additivizations may be considered as a special type of semivalues

additive consistency of risk measures and its application to risk averse routing in networks we investigate the use of risk measures and theories of choice to model risk averse routing and traffic equilibrium on networks with random travel times we interpret the postulates of these theories in the context of routing identifying additive consistency as a plausible condition that allows to reduce risk averse route choice to a standard shortest path problem within the classical theories of choice we show that the only preferences that satisfy this condition are the ones induced by the entropic risk measures

unbounded utility for savage s foundations of statistics and other models a general procedure for extending finite dimensional additive like representations for binary relations to infinite dimensional integral like representations is developed by means of a condition called truncation continuity the restriction of boundedness of utility met throughout the literature can now be dispensed with and for instance normal distributions or any other distribution with finite first moment can be incorporated classical representation results of expected utility such as savage 1954 von neumann and morgenstern 1944 anscombe and aumann 1963 de finetti 1937 and many others can now be extended the results are generalized to schmeidler s 1989 approach with nonadditive measures and choquet integrals and quiggin s 1982 rank dependent utility the different approaches have been brought together in this paper to bring to the fore the unity in the extension process

common mathematical foundations of expected utility and dual utility theories we show that the main results of the expected utility and dual utility theories can be derived in a unified way from two fundamental mathematical ideas the separation principle of convex analysis and integral representations of continuous linear functionals from functional analysis our analysis reveals the dual character of utility functions we also derive new integral representations of dual utility models

dynamic linear programming games with risk averse players motivated by situations in which independent agents wish to cooperate in some uncertain endeavor over time we study dynamic linear programming games which generalize classical linear production games to multi period settings under uncertainty we specifically consider that players may have risk averse attitudes towards uncertainty and model this risk aversion using coherent conditional risk measures for this setting we study the strong sequential core a natural extension of the core to dynamic settings we characterize the strong sequential core as the set of allocations that satisfy a particular finite set of inequalities that depend on an auxiliary optimization model and then leverage this characterization to establish sufficient conditions for emptiness and non emptiness qualitatively whereas the strong sequential core is always non empty when players are risk neutral our results indicate that cooperation in the presence of risk aversion is much more difficult we illustrate this with an application to cooperative newsvendor games where we find that cooperation is possible when it least benefits players and may be impossible when it offers more benefit

new models of decision under uncertainty an interpretative essay the theory of decision under risk and uncertainty has taken a new course in the last ten years the present paper puts these developments into perspective it briefly recalls the experimental results obtained and sketches some of the most important alternative models suggested to fit these results finally a tentative interpretation of all this research movement is offered

what determines the shape of the probability weighting function under uncertainty decision weights are an important component in recent theories of decision making under uncertainty to better explain these decision weights a two stage approach has been proposed first the probability of an event is judged and then this probability is transformed by the probability weighting function known from decision making under risk we extend the two stage approach by allowing the probability weighting function to depend on the type of uncertainty using this more general approach properties of decision weights can be attributed to properties of probability judgments and or to properties of probability weighting we present an empirical study that shows that it is indeed necessary to allow the probability weighting function to be source dependent the analysis includes an examination of properties of the probability weighting function under uncertainty that have not been considered yet

a unified approach to the monotone integral based premium principles under the cpt theory abstract we consider the relationship between different types of the monotone integral based premium principles as a common frame for the cpt premium principle and the mean premium principle the cpt like integral based premium principle is introduced and characterized the jensen type inequalities for the choquet integral and the cpt like premium principle on the class of non negative risks are proven we establish conditions under which the jensen steffensen type inequalities for the cpt premium principle and the cpt like premium principle hold for risks with finite range

semi analytical computation of laplacian green functions in three dimensional domains with disconnected spherical boundaries abstract the generalized method of separation of variables gmsv is applied to solve boundary value problems for the laplace operator in three dimensional domains with disconnected spherical boundaries e g an arbitrary configuration of non overlapping partially reactive spherical sinks or obstacles we consider both exterior and interior problems and all most common boundary conditions dirichlet neumann robin and conjugate one using the translational addition theorems for solid harmonics to switch between the local spherical coordinates we obtain a semi analytical expression of the green function as a linear combination of partial solutions whose coefficients are fixed by boundary conditions although the numerical computation of the coefficients involves series truncation and solution of a system of linear algebraic equations the use of the solid harmonics as basis functions naturally adapted to the intrinsic symmetries of the problem makes the gmsv particularly efficient especially for exterior problems the obtained green function is the key ingredient to solve boundary value problems and to determine various characteristics of stationary diffusion such as reaction rate escape probability harmonic measure residence time and mean first passage time to name but a few the relevant aspects of the numerical implementation and potential applications in chemical physics heat transfer electrostatics and hydrodynamics are discussed

subjective probability and expected utility without additivity comonotic acts are defined and an axiom of comonotomic independence 19 introduced that weakens the von newmann morgenstern axiom of independence if a nondegenerate continuous and monotonic state independent weak order over acts satisfies comonotonic independence then it induces a unique non necessarily additive probability and a von neumann morgenstern utility an extension of theexpected utility theory covers situations as the ellsberg paradox which are inconsistent with additive expected utility the concept of uncertainty aversion and interpretation of comonotonic independence in the context of social welfare functions are included

subdiffusion in a bounded domain with a partially absorbing reflecting boundary the exit time of a subdiffusive process from a bounded domain with a partially absorbing reflecting boundary is considered the short time and long time behaviors of the exit time probability density are investigated by using a spectral decomposition on the basis of the laplace operator eigenfunctions rotation invariant domains are analyzed in depth in order to illustrate the use of theoretical formulas and to compare them to numerical simulations the asymptotic results obtained are relevant for describing subdiffusion inside a living cell with a semipermeable membrane in a chemical reactor filled with catalytic grains of finite reactivity or in mineral or biological samples which are probed by nuclear magnetic resonance measurements subject to surface relaxation

on distributions of functionals of anomalous diffusion paths functionals of brownian motion have diverse applications in physics mathematics and other fields the probability density function pdf of brownian functionals satisfies the feynman kac formula which is a schrodinger equation in imaginary time in recent years there is a growing interest in particular functionals of non brownian motion or anomalous diffusion but no equation existed for their pdf here we derive a fractional generalization of the feynman kac equation for functionals of anomalous paths based on sub diffusive continuous time random walk we also derive a backward equation and a generalization to levy flights solutions are presented for a wide number of applications including the occupation time in half space and in an interval the first passage time the maximal displacement and the hitting probability we briefly discuss other fractional schrodinger equations that recently appeared in the literature

a family of transformed copulas with a singular component abstract in this paper we present a family of bivariate copulas obtained by transforming a given copula function by means of two increasing functions named as transformed copula one distinctive characteristic of the transformed copula is its singular component along the main diagonal conditions guaranteeing the transformed function to be a copula function are provided and several classes of the transformed copulas are given the singular component along the main diagonal of the transformed copula is verified and the tail dependence coefficients of transformed copulas are obtained some properties of the transformed copula are discussed such as the total positivity of order 2 and the concordance order finally conditions for the proposed transformation being invariant are given sufficient conditions guaranteeing that the iterative transformation is a copula function are provided and the convergence of the iterative transformation is proved under some conditions