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We present pricing mechanisms for several online resource allocation problems which obtain tight or nearly tight approximations to social welfare. In our settings, buyers arrive online and purchase bundles of items; buyers' values for the…
Since economic mechanisms are often applied to very different instances of the same problem, it is desirable to identify mechanisms that work well in a wide range of circumstances. We pursue this goal for a position auction setting and…
The present article provides an efficient and accurate hybrid method to price American standard options in certain jump-diffusion models as well as American barrier-type options under the Black & Scholes framework. Our method generalizes…
We consider a one-dimensional Brownian motion of fixed duration $T$. Using a path-integral technique, we compute exactly the probability distribution of the difference $\tau=t_{\min}-t_{\max}$ between the time $t_{\min}$ of the global…
We study online combinatorial auctions with production costs proposed by Blum et al. using the online primal dual framework. In this model, buyers arrive online, and the seller can produce multiple copies of each item subject to a…
We use Lie symmetry methods to price certain types of barrier options. Usually Lie symmetry methods cannot be used to solve the Black-Scholes equation for options because the function defining the maturity condition for an option is not…
We present a mechanism for constructing graphical models, specifically Bayesian networks, from a knowledge base of general probabilistic information. The unique feature of our approach is that it uses a powerful first-order probabilistic…
Developing efficient sequential bidding strategies for repeated auctions is an important practical challenge in various marketing tasks. In this setting, the bidding agent obtains information, on both the value of the item at sale and the…
Pricing options is an important problem in financial engineering. In many scenarios of practical interest, financial option prices associated to an underlying asset reduces to computing an expectation w.r.t.~a diffusion process. In general,…
This paper presents a new asymptotic expansion method for pricing continuously monitoring barrier options. In particular, we develops a semi-group expansion scheme for the Cauchy-Dirichlet problem in the second-order parabolic partial…
We propose a straightforward and effective method for discretizing multi-dimensional diffusion processes as an extension of Milstein scheme. The new scheme is explicitly given and can be simulated using Gaussian variates, requiring the same…
In this paper, we present the first approximation algorithms for the problem of designing revenue optimal Bayesian incentive compatible auctions when there are multiple (heterogeneous) items and when bidders can have arbitrary demand and…
Many algorithms that are originally designed without explicitly considering incentive properties are later combined with simple pricing rules and used as mechanisms. The resulting mechanisms are often natural and simple to understand. But…
We introduce new optimized first-order methods for smooth unconstrained convex minimization. Drori and Teboulle recently described a numerical method for computing the $N$-iteration optimal step coefficients in a class of first-order…
We present a numerical method for the approximation of solutions for the class of stochastic differential equations driven by Brownian motions which induce stochastic variation in fixed directions. This class of equations arises naturally…
In mechanism design it is typical to impose incentive compatibility and then derive an optimal mechanism subject to this constraint. By replacing the incentive compatibility requirement with the goal of minimizing expected ex post regret,…
We consider the classical mathematical economics problem of {\em Bayesian optimal mechanism design} where a principal aims to optimize expected revenue when allocating resources to self-interested agents with preferences drawn from a known…
We provided an analytical representation of the price of a barrier option with one type of special moving barrier. We consider the case that risk free rate, dividend rate and stock volatility are time dependent. We get a pricing formula and…
Barrier derivatives depend on extrema and first-passage events and are therefore highly sensitive to volatility dynamics -- especially to the instantaneous return-volatility correlation $\rho$, often called ``leverage''. This sensitivity…
We introduce a method to exactly generate bridge trajectories for discrete-time random walks, with arbitrary jump distributions, that are constrained to initially start at the origin and return to the origin after a fixed time. The method…