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Estimating win probability is one of the classic modeling tasks of sports analytics. Many widely used win probability estimators use machine learning to fit the relationship between a binary win/loss outcome variable and certain game-state…
Considering the set cover problem, by modifying the approach that gives a logarithmic approximation guarantee for the greedy algorithm, we obtain an estimation of the greedy algorithm's accuracy for a particular input. We compare the…
Approachability has become a standard tool in analyzing earning algorithms in the adversarial online learning setup. We develop a variant of approachability for games where there is ambiguity in the obtained reward that belongs to a set,…
The ``losing positions" of certain combinatorial games constitute linear error detecting and correcting codes. We show that a large class of games that can be cast in the form of *annihilation games*, provides a potentially polynomial…
Our goal here is to discuss the pricing problem of European and American options in discrete time using elementary calculus so as to be an easy reference for first year undergraduate students. Using the binomial model we compute the fair…
This paper describes a class of probabilistic approximation algorithms based on bucket elimination which offer adjustable levels of accuracy and efficiency. We analyze the approximation for several tasks: finding the most probable…
An efficient computational algorithm to price financial derivatives is presented. It is based on a path integral formulation of the pricing problem. It is shown how the path integral approach can be worked out in order to obtain fast and…
We introduce a criterion how to price derivatives in incomplete markets, based on the theory of growth optimal strategy in repeated multiplicative games. We present reasons why these growth-optimal strategies should be particularly relevant…
Options have provided a field of much study because of the complexity involved in pricing them. The Black-Scholes equations were developed to price options but they are only valid for European styled options. There is added complexity when…
Provided a special function of one variable and some of its derivatives can be accurately computed over a finite range, a method is presented to build a series of polynomial approximations of the function with a defined relative error over…
We provide supplementary appendices to the paper Misere quotients for impartial games. These include detailed solutions to many of the octal games discussed in the paper, and descriptions of the algorithms used to compute most of our…
We introduce a new approach for the numerical pricing of American options. The main idea is to choose a finite number of suitable excessive functions (randomly) and to find the smallest majorant of the gain function in the span of these…
Quantitative games are two-player zero-sum games played on directed weighted graphs. Total-payoff games (that can be seen as a refinement of the well-studied mean-payoff games) are the variant where the payoff of a play is computed as the…
We study a setting in which two players play a (possibly approximate) Nash equilibrium of a bimatrix game, while a learner observes only their actions and has no knowledge of the equilibrium or the underlying game. A natural question is…
Options on baskets (linear combinations) of assets are notoriously challenging to price using even the simplest log-normal continuous-time stochastic models for the individual assets. The paper [5] gives a closed form approximation formula…
In online betting, the bookmaker can update the payoffs it offers on a particular event many times before the event takes place, and the updated payoffs may depend on the bets accumulated thus far. We study the problem of bookmaking with…
An open problem posed by the first author is the complexity to decide whether a sequence of nonnegative integer numbers can be the final score of a football tournament. In this paper we propose polynomial time approximate and exponential…
We propose a novel online learning method for minimizing regret in large extensive-form games. The approach learns a function approximator online to estimate the regret for choosing a particular action. A no-regret algorithm uses these…
We consider closed-form approximations for European put option prices within the Heston and GARCH diffusion stochastic volatility models with time-dependent parameters. Our methodology involves writing the put option price as an expectation…
In this paper, we investigate a numerical algorithm for the pricing of swing options, relying on the so-called optimal quantization method. The numerical procedure is described in details and numerous simulations are provided to assert its…