Related papers: Explicit Heston Solutions and Stochastic Approxima…
This work addresses the problem of vehicle path planning in the presence of obstacles and uncertainties, which is a fundamental problem in robotics. While many path planning algorithms have been proposed for decades, many of them have dealt…
This research addresses accurate option pricing by employing models beyond the traditional Black-Scholes framework. While Black-Scholes provides a closed-form solution, it is limited by assumptions of constant volatility, no dividends, and…
In many scientific studies, it becomes increasingly important to delineate the causal pathways through a large number of mediators, such as genetic and brain mediators. Structural equation modeling (SEM) is a popular technique to estimate…
We introduce a new method to price American-style options on underlying investments governed by stochastic volatility (SV) models. The method does not require the volatility process to be observed. Instead, it exploits the fact that the…
We propose an approach to construction of robust non-Euclidean iterative algorithms for convex composite stochastic optimization based on truncation of stochastic gradients. For such algorithms, we establish sub-Gaussian confidence bounds…
Model comparison for the purposes of selection, averaging and validation is a problem found throughout statistics. Within the Bayesian paradigm, these problems all require the calculation of the posterior probabilities of models within a…
In American options, the early exercise feature allows the option to be exercised at any time prior to expiration. However, this flexibility introduces a challenge: the pricing model must value the option while simultaneously determining an…
We develop a new analysis for portfolio optimisation with options, tackling the three fundamental issues with this problem: asymmetric options' distributions, high dimensionality and dependence structure. To do so, we propose a new…
Stochastic gradient descent type methods are ubiquitous in machine learning, but they are only applicable to the optimization of differentiable functions. Proximal algorithms are more general and applicable to nonsmooth functions. We…
We propose the use of statistical emulators for the purpose of valuing mortality-linked contracts in stochastic mortality models. Such models typically require (nested) evaluation of expected values of nonlinear functionals of…
We describe a new, surprisingly simple algorithm, that simulates exact sample paths of a class of stochastic differential equations. It involves rejection sampling and, when applicable, returns the location of the path at a random…
Second-order optimization methods are among the most widely used optimization approaches for convex optimization problems, and have recently been used to optimize non-convex optimization problems such as deep learning models. The widely…
We develop a novel deep learning approach for pricing European options in diffusion models, that can efficiently handle high-dimensional problems resulting from Markovian approximations of rough volatility models. The option pricing partial…
Stochastic, iterative search methods such as Evolutionary Algorithms (EAs) are proven to be efficient optimizers. However, they require evaluation of the candidate solutions which may be prohibitively expensive in many real world…
We propose a new sensitivity analysis methodology for complex stochastic dynamics based on the Relative Entropy Rate. The method becomes computationally feasible at the stationary regime of the process and involves the calculation of…
We develop and analyze several different second-order algorithms for computing a near-optimal solution path of a convex parametric optimization problem with smooth Hessian. Our algorithms are inspired by a differential equation perspective…
Computing shortest paths is one of the most researched topics in algorithm engineering. Currently available algorithms compute shortest paths in mere fractions of a second on continental sized road networks. In the presence of…
In recent years dynamical systems (of deterministic and stochastic nature), describing many models in mathematics, physics, engineering and finances, become more and more complex. Numerical analysis narrowed only to deterministic algorithms…
We introduce a novel signature approach for pricing and hedging path-dependent options with instantaneous and permanent market impact under a mean-quadratic variation criterion. Leveraging the expressive power of signatures, we recast an…
Many least squares problems involve affine equality and inequality constraints. Although there are variety of methods for solving such problems, most statisticians find constrained estimation challenging. The current paper proposes a new…