Advanced Simulation-Based Methods for Optimal Stopping and Control: With Applications in Finance
This is an advanced guide to optimal stopping and control, focusing on advanced Monte Carlo simulation and its application to finance. Written for quantitative finance practitioners and researchers in academia, the book looks at the classical simulation based algorithms before introducing some of the new, cutting edge approaches under development.
An algorithm was developed to generate an ensemble of statistical multiblock AB copolymer chains via a polymer-analogous reaction with acceleration. Ordering in the cylindrical ensemble of such chains is simulated via successive rotation of chains until an arrangement with the maximum energy of attraction between each two nearest chains is attained. The master relation of the ordering and the relations between AA, BB and AB contact fractions were found. Those relations permit to estimate the adequacy of modeling polymers of finite length. Influence of a chain structure, length, and interchain interactions on the ordering efficiency was studied.
The article describes the use of Excel programme for risk assessment models: method of sensitivity analysis, scenarios method, Monte-Carlo method.
long-term investment project, risk, method of sensitivity analysis, Scenario method, method of Monte Carlo simulation
A new variant of the method of probability density distribution recovery for solving topical modeling problems is described. Disadvantages of the Gibbs sampling algorithm are considered, and a modified variant, called the “granulated sampling method,” is proposed. Based on the results of statistical modeling, it is shown that the proposed algorithm is characterized by higher stability as compared to other variants of Gibbs sampling.
In this work, we study the optimal risk sharing problem for an insurer between himself and a reinsurer in a dynamical insurance model known as the Kramer–Lundberg risk process, which, unlike known models, models not per claim reinsurance but rather periodic reinsurance of damages over a given time interval. Here we take into account a natural upper bound on the risk taken by the reinsurer. We solve optimal control problems on an infinite time interval for mean-variance optimality criteria: a linear utility functional and a stationary variation coefficient. We show that optimal reinsurance belongs to the class of total risk reinsurances. We establish that the most profitable reinsurance is the stop-loss reinsurance with an upper limit. We find equations for the values of parameters in optimal reinsurance strategies.
This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.