Related papers: The value of foresight
We obtain option pricing formulas for stock price models in which the drift and volatility terms are functionals of a continuous history of the stock prices. That is, the stock dynamics follows a nonlinear stochastic functional differential…
A new mathematical model for the Black-Scholes equation is proposed to forecast option prices. This model includes new interval for the price of the underlying stock as well as new initial and boundary conditions. Conventional notions of…
In the context of advertising auctions, finding good reserve prices is a notoriously challenging learning problem. This is due to the heterogeneity of ad opportunity types and the non-convexity of the objective function. In this work, we…
Bruss's odds theorem \cite{Bruss1} addresses the problem of determining the optimal stopping time for sequences of independent indicator functions. In this note, we derive upper and lower bounds for the success probability under the optimal…
This paper discusses the revenue management (RM) problem to maximize revenue by pricing items or services. One challenge in this problem is that the demand distribution is unknown and varies over time in real applications such as airline…
For optimal stopping problems with time-inconsistent preference, we measure the inherent level of time-inconsistency by taking the time needed to turn the naive strategies into the sophisticated ones. In particular, when in a repeated…
"How much is my data worth?" is an increasingly common question posed by organizations and individuals alike. An answer to this question could allow, for instance, fairly distributing profits among multiple data contributors and determining…
In economics, there are many ways to describe the interaction between a "seller" and a "buyer". The most common one, with which we interact almost every day, is selling for a fixed price. This option is perfect for selling a mass product,…
The empirically successful Thompson Sampling algorithm for stochastic bandits has drawn much interest in understanding its theoretical properties. One important benefit of the algorithm is that it allows domain knowledge to be conveniently…
We model the joint distribution of choice probabilities and decision times in binary choice tasks as the solution to a problem of optimal sequential sampling, where the agent is uncertain of the utility of each action and pays a constant…
As a firm varies the price of a product, consumers exhibit reference effects, making purchase decisions based not only on the prevailing price but also the product's price history. We consider the problem of learning such behavioral…
Long term investment is one of the major investment strategies. However, calculating intrinsic value of some company and evaluating shares for long term investment is not easy, since analyst have to care about a large number of financial…
We study the problem of setting a price for a potential buyer with a valuation drawn from an unknown distribution $D$. The seller has "data"' about $D$ in the form of $m \ge 1$ i.i.d. samples, and the algorithmic challenge is to use these…
We consider an individual or household endowed with an initial capital and an income, modeled as a linear function of time. Assuming that the discount rate evolves as an Ornstein-Uhlenbeck process, we target to find an unrestricted…
In this paper we study optimal investment when the investor can peek some time units into the future, but cannot fully take advantage of this knowledge because of quadratic transaction costs. In the Bachelier setting with exponential…
Opportunistic detection rules (ODRs) are variants of fixed-sample-size detection rules in which the statistician is allowed to make an early decision on the alternative hypothesis opportunistically based on the sequentially observed…
People often face trade-offs between costs and benefits occurring at various points in time. The predominant discounting approach is to use the exponential form. Central to this approach is the discount rate, a unique parameter that…
We show that strategies implemented in automatic theorem proving involve an interesting tradeoff between execution speed, proving speedup/computational time and usefulness of information. We advance formal definitions for these concepts by…
A seller sells an object over time but is uncertain how the buyer learns their willingness-to-pay. We consider informational robustness under \textit{limited commitment}, where the seller offers a price \textit{each period} to maximize…
We consider the problem of a single seller repeatedly selling a single item to a single buyer (specifically, the buyer has a value drawn fresh from known distribution $D$ in every round). Prior work assumes that the buyer is fully rational…