01979nam a2200193   450000500170000002000180001704100120003508200200004708400250006710000220009224501360011425000060025026000440025630000100030050010800031050503200139065000450171070000300175520260421144045.0  a9781009503105  aEnglish  a332.0151bLIP/H  2Colon Classification  aLipton, Alexander  aHydrodynamics of Markets: Hidden Links between Physics and Finance (Elements in Quantitative Finance)cEdited by Riccardo Rebonato   a1  aUK:bCambridge University Press,c2024.  a138p.  aAn intriguing link between a wide range of problems occurring in physics and financial engineering is presented. These problems include the evolution of small perturbations of linear flows in hydrodynamics, the movements of particles in random fields described by the Kolmogorov and Klein-Kramers equations, the Ornstein-Uhlenbeck and Feller processes, and their generalizations. They are reduced to affine differential and pseudo-differential equations and solved in a unified way by using Kelvin waves and developing a comprehensive math framework for calculating transition probabilities and expectations. Kelvin waves are instrumental for studying the well-known Black-Scholes, Heston, and Stein-Stein models and more complex path-dependent volatility models, as well as the pricing of Asian options, volatility and variance swaps, bonds, and bond options. Kelvin waves help to solve several cutting-edge problems, including hedging the impermanent loss of Automated Market Makers for cryptocurrency trading. This title is also available as Open Access on Cambridge Core.  aContents

1. Introduction 
2. Fluid Flows 
3. Kolmogorov Stochastic Process 
4. Klein–Kramers Stochastic Process 
5. Transition Probability Densities for Stochastic Processes
6. Gaussian Stochastic Processes 
7. Non-Gaussian Stochastic Processes 
8. Pricing of Financial Instruments
9. Conclusions 
   References   aEconomics- Markets- Quantitative Finance  a Rebonato, Riccardo (ed.)