Related papers: Watermark Options
In this article we discuss the problem of calculating optimal model-independent (robust) bounds for the price of Asian options with discrete and continuous averaging. We will give geometric characterisations of the maximising and the…
We investigate the (functional) convex order of for various continuous martingale processes, either with respect to their diffusions coefficients for L\'evy-driven SDEs or their integrands for stochastic integrals. Main results are bordered…
An abstract framework guaranteeing the continuous differentiability of local value functions on $H^1(\Omega)$ associated with optimal stabilization problems subject to abstract semilinear parabolic equations in the presence of norm…
As is known, the problems for the differential equations with continuously changing order of the derivatives are not considered completely. In this paper we consider the initial and boundary value problems for this type of linear ordinary…
We characterize the behavior of the solutions of linear evolution partial differential equations on the half line in the presence of discontinuous initial conditions or discontinuous boundary conditions, as well as the behavior of the…
Recent work in the literature has studied fourth-order elliptic operators on manifolds with boundary. This paper proves that, in the case of the squared Laplace operator, the boundary conditions which require that the eigenfunctions and…
We introduce the most general class of linear boundary-value problems for systems of first-order ordinary differential equations whose solutions belong to the complex H\"older space $C^{n+1,\alpha}$, with $0\leq n\in\mathbb{Z}$ and…
We propose a deep learning algorithm for high dimensional optimal stopping problems. Our method is inspired by the penalty method for solving free boundary PDEs. Within our approach, the penalized PDE is approximated using the Deep BSDE…
We consider a market model where there are two levels of information. The public information generated by the financial assets, and a larger flow of information that contains additional knowledge about a random time. This random time can…
Expanding the ideas of the author's paper 'Nonexpansive maps and option pricing theory' (Kibernetica 34:6 (1998), 713-724) we develop a pure game-theoretic approach to option pricing, by-passing stochastic modeling. Risk neutral…
An important problem of optimization analysis surges when parameters such as $ \{\theta_j\}_{j=1,\, \dots \,,k }$, determining a function $ y=f(x\given\{\theta_j\}) $, must be estimated from a set of observables $ \{ x_i,y_i\}_{i=1,\, \dots…
We study initial-boundary value problems for linear evolution equations of arbitrary spatial order, subject to arbitrary linear boundary conditions and posed on a rectangular 1-space, 1-time domain. We give a new characterisation of the…
Optimal stopping is the problem of determining when to stop a stochastic system in order to maximize reward, which is of practical importance in domains such as finance, operations management and healthcare. Existing methods for…
This thesis develops a new framework for modelling price processes in finance, such as an equity price or foreign exchange rate. This can be related to the conventional Ito calculus-based framework through the time integral of a price's…
A general, variational approach to derive low-order reduced systems is presented. The approach is based on the concept of optimal parameterizing manifold (OPM) that substitutes the more classical notions of invariant or slow manifold when…
In this work we propose a novel approach to investigate boundary value problems (BVPs) for fully third order differential equations. It is based on the reduction of BVPs to operator equations for the nonlinear terms but not for the…
This paper proves continuity of value functions in discounted periodic-review single-commodity total-cost inventory control problems with \revision{continuous inventory levels,} fixed ordering costs, possibly bounded inventory storage…
We consider the initial boundary value problem for free-evolution formulations of general relativity coupled to a parametrized family of coordinate conditions that includes both the moving puncture and harmonic gauges. We concentrate…
In this article we study a class of generalised linear systems of difference equations with given boundary conditions and assume that the boundary value problem is non-consistent, i.e. it has infinite many or no solutions. We take into…
We study the optimal portfolio liquidation problem over a finite horizon in a limit order book with bid-ask spread and temporary market price impact penalizing speedy execution trades. We use a continuous-time modeling framework, but in…