Parameter estimation in differential equation models is a critical endeavour in the mathematical modelling of dynamic systems. Such models, represented by ordinary differential equations (ODEs), ...
Stochastic differential equations have been shown useful in describing random continuous time processes. Biomedical experiments often imply repeated measurements on a series of experimental units and ...
Delay differential equations (DDEs) are widely used in ecology, physiology and many other areas of applied science. Although the form of the DDE model is usually proposed based on scientific ...
The Navier–Stokes partial differential equation was developed in the early 19th century by Claude-Louis Navier and George ...
Cancer is viewed as a multistep process whereby a normal cell is transformed into a cancer cell through the acquisition of mutations. We reduce the complexities of cancer progression to a simple set ...
In this paper we examine the capacity of arbitrage-free neural stochastic differential equation market models to produce realistic scenarios for the joint dynamics of multiple European options on a ...
For the description of complex dynamical systems, data-driven modeling and AI are gaining increasing importance. In this context, large data sets from experiments and computer simulations are ...
Calibration of local-stochastic and path-dependent volatility models to vanilla and no-touch options
In this paper, we consider a large class of continuous semi-martingale models and propose a generic framework for their simultaneous calibration to vanilla and no-touch options. The method builds on ...
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