In actuarial science, collective risk models, in which the aggregate claim amount of a portfolio is defined in terms of random sums, play a crucial role. In these models, it is common to assume that the number of claims and their amounts are independent, even if this might not always be the...

We show that an explicit approximate implied volatility formula can be obtained from a Black–Scholes formula approximation that is 2% accurate. The relative error of the approximate implied volatility is uniformly bounded for options with any moneyness and with arbitrary large or small option...

A new methodology for calibrating parameters when working with intractable, dynamic structural models is developed. A straight-forward extension also allows for formal estimation and hypothesis testing in a Generalized Method of Moment framework. The method is based on multigrid techniques used...

As China develops its derivatives and financial services industry it will be necessary for it to create an infrastructure for financial computing. Traditional proprietary models of software development may prove unsuitable as they treat the user of the software as a passive agent rather than as...

We propose a new method for solving high-dimensional dynamic programming problems and recursive competitive equilibria with a large (but finite) number of heterogeneous agents using deep learning. The "curse of dimensionality" is avoided due to four complementary techniques: (1) exploiting...

We provide a survey of recent results on model calibration by Optimal Transport. We present the general framework and then discuss the calibration of local, and local-stochastic, volatility models to European options, the joint VIX/SPX calibration problem as well as calibration to some...

We propose a new method for solving high-dimensional dynamic programming problems and recursive competitive equilibria with a large (but finite) number of heterogeneous agents using deep learning. The „curse of dimensionality“ is avoided due to four complementary techniques: (1) exploiting...

The no Butterfly arbitrage domain of Gatheral SVI 5-parameters formula for the volatility smile has been recently described. It requires in general a numerical minimization of 2 functions altogether with a few root finding procedures. We study here the case of some sub-SVIs (all with 3...

In this work we illustrate a simple logical framework serving the purpose of measuring value creation in a real-life solar photovoltaic project, funded with a lease contract, a loan contract and internal financing (i.e., withdrawal from liquid assets). We use the projected accounting data to...

The main purpose of this article is to present the use of R programming language in cartographic visualization demonstrating using machine learning methods in geographic education. Current trends in education technologies are largely influenced by the possibilities of distance-learning,...