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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…
In this work, we study the optimization problem of a renewable resource in finite time. The resource is assumed to evolve according to a logistic stochastic differential equation. The manager may harvest partially the resource at any time…
This chapter reviews standard parameter-estimation techniques and presents a novel gradient-, ensemble-, adjoint-free data-driven parameter estimation technique in the DDDAS framework. This technique, called retrospective cost parameter…
We propose an analytically tractable class of models for the dynamics of a limit order book, described through a stochastic partial differential equation (SPDE) with multiplicative noise for the order book centered at the mid-price, along…
A nonlinear inequality is formulated in the paper. An estimate of the rate of decay of solutions to this inequality is obtained. This inequality is of interest in a study of dynamical systems and nonlinear evolution equations. It can be…
This paper develops a probabilistic numerical method for solution of partial differential equations (PDEs) and studies application of that method to PDE-constrained inverse problems. This approach enables the solution of challenging inverse…
The question of pricing and hedging a given contingent claim has a unique solution in a complete market framework. When some incompleteness is introduced, the problem becomes however more difficult. Several approaches have been adopted in…
The purpose of this review paper is to present our recent results on nonlinear and nonlocal mathematical models arising from modern financial mathematics. It is based on our four papers written jointly by J. Cruz, M. Grossinho, D. Sevcovic,…
Estimation of tail quantities, such as expected shortfall or Value at Risk, is a difficult problem. We show how the theory of nonlinear expectations, in particular the Data-robust expectation introduced in [5], can assist in the…
In this work we present a new method to compute the delays of delay differential equations (DDEs), such that the DDE has a purely imaginary eigenvalue. For delay differential equations with multiple delays, the critical curves or critical…
This paper proposes an unconditionally stable numerical method for solving a nonlinear Sobolev model with distributed delay. The proposed computational approach approximates the time derivative by interpolation technique whereas the spatial…
Recent advances in learning dynamical systems from data have shown significant promise. However, many existing methods assume access to the full state of the system -- an assumption that is rarely satisfied in practice, where systems are…
Mathematical models of interacting populations are often constructed as systems of differential equations, which describe how populations change with time. Below we study one such model connected to the nonlinear dynamics of a system of…
We study time consistent dynamic pricing mechanisms of European contingent claims under uncertainty by using G framework introduced by Peng ([24]). We consider a financial market consisting of a riskless asset and a risky stock with price…
This paper presents machine learning techniques and deep reinforcement learningbased algorithms for the efficient resolution of nonlinear partial differential equations and dynamic optimization problems arising in investment decisions and…
G-expectation, as a sublinear expectation, provides a powerful framework for modeling uncertainty in financial markets. Motivated by the need for robust valuation under model uncertainty, this work develops a unified risk-neutral valuation…
SABR models have been used to incorporate stochastic volatility to LIBOR market models (LMM) in order to describe interest rate dynamics and price interest rate derivatives. From the numerical point of view, the pricing of derivatives with…
Data-driven methodologies are nowadays ubiquitous. Their rapid development and spread have led to applications even beyond the traditional fields of science. As far as dynamical systems and differential equations are concerned, neural…
An important problem in project management is determining ways to distribute amongst activities the costs that are incurred when a project is delayed because some activities end later than expected. In this study, we address this problem in…
The Sparse Identification of Nonlinear Dynamics (SINDy) framework is a robust method for identifying governing equations, successfully applied to ordinary, partial, and stochastic differential equations. In this work we extend SINDy to…