Heat kernel perturbation theory is a tool for constructing explicit approximation formulas for the solutions of linear parabolic equations. We review the crux of this perturbative formalism and then apply it to differential equations which govern the transition densities of several local...

We propose how to quantify high-frequency market sentiment using high-frequency news from NASDAQ news platform and support vector machine classifiers. News arrive at markets randomly and the resulting news sentiment behaves like a stochastic process. To characterize the joint evolution of...

… a nice book for researchers and practitioners. … this book can be regarded as a wonderful application of stochastic analysis, as it includes not only detailed theoretical proofs but also practical illustrative examples. With the systematic and feasible numeraire techniques, the book can...

chapter 1 Elements of Finance -- chapter 2 Binomial Models -- chapter 3 Diffusion Models -- chapter 4 Interest Rate Contracts -- chapter 5 Barrier Options -- chapter 6 Lookback Options -- chapter 7 American Options -- chapter 8 Contracts on Three or More Assets: Quantos, Rainbows and "Friends"...