Properties of the Ornstein-Uhlenbeck bridge

Sylvain Corlay (1)

1 Bloomberg L.P. Quantitative Finance Research

This paper presents a study of the properties of the Ornstein-Uhlenbeck bridge, specifically, we derive its Karhunen-Loève expansion for any value of the initial variance and mean-reversion parameter (or mean-repulsion if negative). We also show that its canonical decomposition can be obtained using some techniques related to generalized bridges. Finally, we present an application to the optimal functional quantization of the Ornstein-Uhlenbeck bridge.

Keywords: Ornstein-Uhlenbeck bridge; canonical decomposition; Karhunen-Loève; filtration enlargement; functional quantization

Domains: Probability [math.PR]

Sylvain Corlay. Properties of the Ornstein-Uhlenbeck bridge. 2013. ⟨hal-00875342v4⟩