This paper presents an extensive test of the Libor Market on the Euro Cap and Swaption market. The deterministic LIBOR market model prices OTC cap exactly and prices OTC swaptions with errors well below two basis points. Tests for the hedging performance show that the deterministic LIBOR market...

In this paper the issue of mathematical programming and optimization has being revisited. The theory of optimization deals with the development of models and methods that determine optimal solutions to mathematical problems defined. Mathematical model must be some function of any solution that...

Methods for leader's detection and overthrow in networks are useful tools for decision-making in many real-life cases, such as criminal networks with hidden patterns or money laundering networks. In the given research, we represent the algorithms that detect and overthrow the most influential...

Most important economic decision problems are sequential, and thus naturally represented as Markov Decision Problems (MDP). After reviewing the theory of MDPs, the applicability of MDPs to real-life sequential decisions appears impractical. The central question addressed in this essay is how...

This paper addresses the joint calibration problem of SPX options and VIX options or futures. We show that the problem can be formulated as a semimartingale optimal transport problem under a finite number of discrete constraints, in the spirit of [arXiv:1906.06478]. We introduce a PDE...

In an environment with stocks and short-term debt, random changes in the risk-reward frontier produce hedging demands for equities, implying that portfolio policies supporting optimal life-cycle consumption are rarely mean-variance efficient. Pursuing optimal life-cycle portfolio policies is...

Traditional portfolio optimization approaches suffer from the drawback of often leading to highly concentrated portfolios. We propose a new kind of optimization focusing on a homogeneous distribution of risk among the portfolio constituents. We describe the underlying ideas of the approach and...

We give a functional description of the space of stochastic integrals with respect to a given family of martingales, based on the notion of direct integral of Hilbert spaces. We define the multiplicity function of a filtration and show, using our Hilbert space construction, that the multiplicity...

We use minority game model to investigate evolutionary dynamics in complex networks of adaptive agents competing for limited resources. We show that the dynamics and the associated phase structures critically depend on the underlying network organizations, and evolution is a key mechanism for...