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We examine the problem of estimating the trace of a matrix $A$ when given access to an oracle which computes $x^\dagger A x$ for an input vector $x$. We make use of the basis vectors from a set of mutually unbiased bases, widely studied in…
We consider as given a discrete time financial market with a risky asset and options written on that asset and determine both the sub- and super-hedging prices of an American option in the model independent framework of ArXiv:1305.6008. We…
Sobol' sensitivity index estimators for stochastic models are functions of nested Monte Carlo estimators, which are estimators built from two nested Monte Carlo loops. The outer loop explores the input space and, for each of the…
The paper introduces a new estimation method for the standard linear regression model. The procedure is not driven by the optimisation of any objective function rather, it is a simple weighted average of slopes from observation pairs. The…
Differential equations can be used to construct predictive models of a diverse set of real-world phenomena like heat transfer, predator-prey interactions, and missile tracking. In our work, we explore one particular application of…
This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…
In this paper we provide a comprehensive analysis of a structural model for the dynamics of prices of assets traded in a market originally proposed in [1]. The model takes the form of an interacting generalization of the geometric Brownian…
Price determination is a central research topic of revenue management in marketing. The important aspect in pricing is controlling the stochastic behavior of demand, and the previous studies have tackled price optimization problems with…
We address the problem of strategic asset allocation (SAA) with portfolios that include illiquid alternative asset classes. The main challenge in portfolio construction with illiquid asset classes is that we do not have direct control over…
Market makers provide liquidity to other market participants: they propose prices at which they stand ready to buy and sell a wide variety of assets. They face a complex optimization problem with both static and dynamic components. They…
This article introduces an intrinsic entropy model that can be used as an indicator to gauge investor interest in a given exchange-traded security, along with the state of the general market corroborated by individual security trade data.…
What types of numeric representations emerge in neural systems, and what would a satisfying answer to this question look like? In this work, we interpret Neural Network (NN) solutions to sequence based number tasks using a variety of…
We present a new nonparametric mixture-of-experts model for multivariate regression problems, inspired by the probabilistic k-nearest neighbors algorithm. Using a conditionally specified model, predictions for out-of-sample inputs are based…
This thesis develops a mathematical framework for the analysis of continuous-time trading strategies which, in contrast to the classical setting of continuous-time finance, does not rely on stochastic integrals or other probabilistic…
This paper describes a new approach to solving some stochastic optimization problems for linear dynamic system with various parametric uncertainties. Proposed approach is based on application of tensor formalism for creation the…
We introduce a new method for the estimation of the angular parameters [i.e., central directions of arrival (DOAs) and angular spreads] of multiple non-circular and incoherently-distributed (ID) sources and thoroughly analyze its…
Option prices encode the market's collective outlook through implied density and implied volatility. An explicit link between implied density and implied volatility translates the risk-neutrality of the former into conditions on the latter…
Modelling is an essential procedure in analyzing and controlling a given logical dynamic system (LDS). It has been proved that deterministic LDS can be modeled as a linear-like system using algebraic state space representation. However, due…
In this paper we are concerned with fully automatic and locally adaptive estimation of functions in a "signal + noise"-model where the regression function may additionally be blurred by a linear operator, e.g. by a convolution. To this end,…
Black-Scholes (BS) is the standard mathematical model for option pricing in financial markets. Option prices are calculated using an analytical formula whose main inputs are strike (at which price to exercise) and volatility. The BS…