In the recent econophysics literature, the use of functional integrals is widespread for the calculation of option prices. In this paper, we extend this approach in several directions by means of δ-function perturbations. First, we show that results about infinitely repulsive δ-function are...

Functional integrals constitute a powerful tool in the investigation of financial models. In the recent econophysics literature, this technique was successfully used for the pricing of a number of derivative securities. In the present contribution, we introduce this approach to the field of...

In this paper, we investigate the transition probabilities for diffusion processes. In a first part, we show how transition probabilities for rather general diffusion processes can always be expressed by means of a path integral. For several classical models, an exact calculation is possible,...

This paper concerns optimal asset-liability management when the assets and the liabilities are modeled by means of correlated geometric Brownian motions as suggested in Gerber and Shiu [2003. Geometric Brownian motion models for assets and liabilities: from pension funding to optimal dividends....

In this paper, we investigate the transition probabilities for diffusion processes. In a first part, we show how transition probabilities for rather general diffusion processes can always be expressed by means of a path integral. For several classical models, an exact calculation is possible,...

In a recent paper, Salminen and Yor (2004b) relate the distribution of the Dufresne's reflected perpetuity to the hitting time of a reflected Bessel process. In this contribution, we adapt the results of Salminen and Yor (2004b) in several ways. First, we use spectral theory to obtain a series...

Under most local and stochastic volatility models the underlying forward is assumed to be a positive function of a time-changed Brownian motion. It relates nicely the implied volatility smile to the so-called activity rate in the market. Following Young and DeWitt-Morette (1986) [8], we propose...