Related papers: Utility function estimation: the entropy approach
The entropy is a measure of uncertainty that plays a central role in information theory. When the distribution of the data is unknown, an estimate of the entropy needs be obtained from the data sample itself. We propose a semi-parametric…
We perform a stability analysis for the utility maximization problem in a general semimartingale model where both liquid and illiquid assets (random endowments) are present. Small misspecifications of preferences (as modeled via expected…
Data-driven decision making plays an important role even in high stakes settings like medicine and public policy. Learning optimal policies from observed data requires a careful formulation of the utility function whose expected value is…
Maximization of an expensive, unimodal function under random observations has been an important problem in hyperparameter tuning. It features expensive function evaluations (which means small budgets) and a high level of noise. We develop…
We propose a continuous-time nonlinear model of opinion dynamics with utility-maximizing agents connected via a social influence network. A distinguishing feature of the proposed model is the inclusion of an opinion-dependent…
The well known maximum-entropy principle due to Jaynes, which states that given mean parameters, the maximum entropy distribution matching them is in an exponential family, has been very popular in machine learning due to its "Occam's…
We examine behavioral axioms in decision theory that are satisfied approximately rather than exactly. We demonstrate that in key domains -- decisions under risk, uncertainty, and intertemporal choice -- behavior that \emph{almost} satisfies…
We study the utility maximization problem for power utility random fields in a semimartingale financial market, with and without intermediate consumption. The notion of an opportunity process is introduced as a reduced form of the value…
Orseau and Ring, as well as Dewey, have recently described problems, including self-delusion, with the behavior of agents using various definitions of utility functions. An agent's utility function is defined in terms of the agent's history…
The concept of Shannon Entropy for probability distributions and associated Maximum Entropy Principle are extended here to the concepts of Relative Divergence of one Grading Function from another and Maximum Relative Divergence Principle…
Recommendation systems are widespread, and through customized recommendations, promise to match users with options they will like. To that end, data on engagement is collected and used. Most recommendation systems are ranking-based, where…
To study the assumption that the utility maximization hypothesis implicitly adds to consumer theory, we consider a mathematical representation of pre-marginal revolution consumer theory based on subjective exchange ratios. We introduce two…
We study the problem of maximising terminal utility for an agent facing model uncertainty, in a frictionless discrete-time market with one safe asset and finitely many risky assets. We show that an optimal investment strategy exists if the…
The main objective of dose finding trials is to find an optimal dose amongst a candidate set for further research. The trial design in oncology proceeds in stages with a decision as to how to treat the next group of patients made at every…
We consider a continuous-time market with proportional transaction costs. Under appropriate assumptions we prove the existence of optimal strategies for investors who maximize their worst-case utility over a class of possible models. We…
Richard Cox [1] set the axiomatic foundations of probable inference and the algebra of propositions. He showed that consistency within these axioms requires certain rules for updating belief. In this paper we use the analogy between…
Different from shopping at retail stores, consumers on e-commerce platforms usually cannot touch or try products before purchasing, which means that they have to make decisions when they are uncertain about the outcome (e.g., satisfaction…
We study the dual formulation of the utility maximization problem in incomplete markets when the utility function is finitely valued on the whole real line. We extend the existing results in this literature in two directions. First, we…
The method of maximum entropy (ME) is extended to address the following problem: Once one accepts that the ME distribution is to be preferred over all others, the question is to what extent are distributions with lower entropy supposed to…
We consider the weighted least squares spline approximation of a noisy dataset. By interpreting the weights as a probability distribution, we maximize the associated entropy subject to the constraint that the mean squared error is…