Feynman–kac Formulas for Black–Scholes–Type Operators

By Svante Janson, Johan Tysk. 2006

77 citations recorded by the source corpus.

Subfields: Applied Mathematics, Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6b466f93c3f917fc9c7c6e8399ece3f6eb2c2f6f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Ioannis Karatzas
2. J. Ruf
3. Daniel Fernholz
4. Erik Ekström
5. Chao Zhu
6. Johan Tysk
7. Charles-Edouard Br'ehier

In Finance

1. Ioannis Karatzas
2. J. Ruf
3. Erik Ekström
4. Daniel Fernholz
5. Johan Tysk
6. George Yin
7. Chao Zhu
8. Nicholas A. Baran

In Mathematical Physics

1. Ioannis Karatzas
2. J. Ruf
3. Daniel Fernholz
4. Erik Ekström
5. George Yin
6. Chao Zhu
7. Johan Tysk

Citations in the corpus

• The Black–Scholes equation in stochastic volatility models (2010, background): “Indeed, in [13], the connection between the option price given as a risk-neutral expected value and the corresponding BlackScholes equation is made precise for options on several underlying assets in a local volatility model with absorbing boundary conditions.”
• Feynman–Kac formulas for regime-switching jump diffusions and their applications (2015, background): “Numerous applications have been found; see, for example, [7, 10, 18] (finance), [2, 28] (DNA breathing dynamics, physics, and computer science), and [9] (statistical physics, biology, and engineering problems).”
• Bubbles, convexity and the Black–Scholes equation (2009, background): “The main result of this section says that the option price u(x, t) given by (2) is indeed a classical solution to (3)–(5); compare [17] for the standard case.”
• Optimal arbitrage under model uncertainty. (2011, methodology): “Using results from the theory of stochastic flows [Kunita (1990), Protter (2004)] and from parabolic partial differential equations [Janson and Tysk (2006), Ekström and Tysk (2009)], Theorem 2 in Ruf (2011) shows that the function Γ(·, ·) is then of class C1,2 locally on (0,∞) × (0,∞)n, and solves…”
• Distribution of the time to explosion for one-dimensional diffusions (2013, methodology): “The proof of Proposition 5.2 resembles the arguments in Janson and Tysk (2006).”
• HEDGING UNDER ARBITRAGE (2010, unknown): “Friedman (1976), Chapters 6 and 15 and Janson and Tysk (2006) have related results, but they imposelinear growth conditions ona(·, ·) so that PDE (4.2) has a unique solution of polynomial growth.”