Related papers: Variance optimal hedging for continuous time addit…
Importance sampling has been known as a powerful tool to reduce the variance of Monte Carlo estimator for rare event simulation. Based on the criterion of minimizing the variance of Monte Carlo estimator within a parametric family, we…
We study the existence theory for parabolic variational inequalities in weighted $L^2$ spaces with respect to excessive measures associated with a transition semigroup. We characterize the value function of optimal stopping problems for…
We present a theory of option pricing and hedging, designed to address non-perfect arbitrage, market friction and the presence of `fat' tails. An implied volatility `smile' is predicted. We give precise estimates of the residual risk…
We design and analyze a Schwarz waveform relaxation algorithm for domain decomposition of advection-diffusion-reaction problems with strong heterogeneities. The interfaces are curved, and we use optimized Robin or Ventcell transmission…
We investigate the techniques and ideas used in the convergence analysis of two proximal ADMM algorithms for solving convex optimization problems involving compositions with linear operators. Besides this, we formulate a variant of the ADMM…
We propose a hedging approach for general contingent claims when liquidity is a concern and trading is subject to transaction cost. Multiple assets with different liquidity levels are available for hedging. Our risk criterion targets a…
Variable selection is fundamental to high-dimensional statistical modeling. Many variable selection techniques may be implemented by maximum penalized likelihood using various penalty functions. Optimizing the penalized likelihood function…
We derive a new high-order compact finite difference scheme for option pricing in stochastic volatility models. The scheme is fourth-order accurate in space and second-order accurate in time. Under some restrictions, theoretical results…
We prove necessary optimality conditions of Euler-Lagrange type for a problem of the calculus of variations with time delays, where the delay in the unknown function is different from the delay in its derivative. Then, a more general…
We describe an apparatus for subgradient-following of the optimum of convex problems with variational penalties. In this setting, we receive a sequence $y_i,\ldots,y_n$ and seek a smooth sequence $x_1,\ldots,x_n$. The smooth sequence needs…
We study more general variational problems on time scales. Previous results are generalized by proving necessary optimality conditions for (i) variational problems involving delta derivatives of more than the first order, and (ii) problems…
Additive models belong to the class of structured nonparametric regression models that do not suffer from the curse of dimensionality. Finding the additive components that are nonzero when the true model is assumed to be sparse is an…
The research presented in this article provides an alternative option pricing approach for a class of rough fractional stochastic volatility models. These models are increasingly popular between academics and practitioners due to their…
We present an algorithm to approximate the solutions to variational problems where set of admissible functions consists of convex functions. The main motivator behind this numerical method is estimating solutions to Adverse Selection…
In the setting of additive regression model for continuous time process, we establish the optimal uniform convergence rates and optimal asymptotic quadratic error of additive regression. To build our estimate, we use the marginal…
We present a new family of min-max optimization algorithms that automatically exploit the geometry of the gradient data observed at earlier iterations to perform more informative extra-gradient steps in later ones. Thanks to this adaptation…
We deal with direct and inverse problems of the calculus of variations on arbitrary time scales. Firstly, using the Euler-Lagrange equation and the strengthened Legendre condition, we give a general form for a variational functional to…
This is the second part of study on the optimal convergence rate of the explicit Euler discretization in time for the convection-diffusion equations [Appl. Math. Lett. \textbf{131} (2022) 108048] which focuses on high-dimensional…
In a stochastic volatility framework, we find a general pricing equation for the class of payoffs depending on the terminal value of a market asset and its final quadratic variation. This allows a pricing tool for European-style claims…
A new algorithm is presented for solving the soft-margin Support Vector Machine (SVM) optimization problem with an $\ell^{1}$ penalty. This algorithm is designed to require a modest number of passes over the data, which is an important…