Showing results for "Stochastic Optimization in Insurance A Dynamic Programming Approach Pablo Azcue German"

The main purpose of the book is to show how a viscosity approach can be used to tackle control problems in insurance. The problems covered are the maximization of survival probability as well as the maximization of dividends in the classical collective risk model. The authors consider the possibility of controlling the risk process by reinsurance as well as by investments. They show that optimal value functions are characterized as either the unique or the smallest viscosity solution of th...

This book studies a general class of convex stochastic optimization (CSO) problems that unifies many common problem formulations from operations research, financial mathematics and stochastic optimal control. We extend the theory of dynamic programming and convex duality to allow for a unified and simplified treatment of various special problem classes found in the literature. The extensions allow also for significant generalizations to existing problem formulations. Both dynamic programmi...

This volume presents a collection of contributions dedicated to applied problems in the financial and energy sectors that have been formulated and solved in a stochastic optimization framework. The invited authors represent a group of scientists and practitioners, who cooperated in recent years to facilitate the growing penetration of stochastic programming techniques in real-world applications, inducing a significant advance over a large spectrum of complex decision problems.After...

This new volume examines the rapidly evolving landscape of financial innovation shaped by digital technologies. From mobile payments and robo-advisory services to decentralized finance (DeFi) and asset tokenization, the book captures the breadth of transformation redefining how financial systems operate. It presents a balanced exploration of both opportunities and challenges, highlighting how fintech is expanding access, improving efficiency, and reshaping traditional financial structures....

This book examines optimization problems that in practice involve random model parameters. It outlines the computation of robust optimal solutions, i.e., optimal solutions that are insensitive to random parameter variations, where appropriate deterministic substitute problems are needed. Based on the probability distribution of the random data and using decision theoretical concepts, optimization problems under stochastic uncertainty are converted into corresponding deterministic problems....

This book introduces the basic concepts and tools of dynamic optimization as used in economics. The book emphasizes intuition, gradually adding small doses of mathematical development as needed to provide an accessible stand-alone introduction to the topic. All three primary approaches to dynamic optimization are covered: the calculus of variations, optimal control theory and dynamic programming. Numerous examples from the economics literature are presented, along with reference to key his...

Pyramid Algorithms presents a unique approach to understanding, analyzing, and computing the most common polynomial and spline curve and surface schemes used in computer-aided geometric design, employing a dynamic programming method based on recursive pyramids.The recursive pyramid approach offers the distinct advantage of revealing the entire structure of algorithms, as well as relationships between them, at a glance. This book-the only one built around this approach-is certain to change ...

This book presents a comprehensive series of methods in nonsmooth optimization, with a particular focus on their application in stochastic programming and dedicated algorithms for decision-making under uncertainty. Each method is accompanied by rigorous mathematical analysis, ensuring a deep understanding of the underlying principles. The theoretical discussions included are essential for comprehending the mechanics of various algorithms and the nature of the solutions they provide—whether...

This book examines optimization problems that in practice involve random model parameters. It details the computation of robust optimal solutions, i.e., optimal solutions that are insensitive with respect to random parameter variations, where appropriate deterministic substitute problems are needed. Based on the probability distribution of the random data and using decision theoretical concepts, optimization problems under stochastic uncertainty are converted into appropriate deterministic...

I wanted to compute 80th term of the Fibonacci series. I wrote the rampant recursive function,int fib(int n){ return (1==n 2==n) ? 1 : fib(n-1) + fib(n-2);}and waited for the result. I wait… and wait… and wait…With an 8GB RAM and an Intel i5 CPU, why is it taking so long? I terminated the process and tried computing the 40th term. It took about a second. I put a check and was shocked to find that the above recursive function was called 204,668,309 times while computing the 40th term. More t...

Multistage stochastic optimization problems appear in many ways in finance, insurance, energy production and trading, logistics and transportation, among other areas. They describe decision situations under uncertainty and with a longer planning horizon. This book contains a comprehensive treatment of today’s state of the art in multistage stochastic optimization. It covers the mathematical backgrounds of approximation theory as well as numerous practical algorithms and examples for the ge...

Embark on a structured journey through the world of financial mathematics with this comprehensive guide. This book provides a solid foundation in the essential principles and methods required for sound financial analysis and decision-making.Beginning with the mathematical fundamentals of finance, you will explore core concepts such as interest and compound interest calculations, annuity and amortization accounting, as well as present and future value determinations. The text further...