  An 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.
