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2 Applicationes Mathematicae

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A recursive robust Bayesian estimation in partially observed financial market

100%

Huang J.

Applicationes Mathematicae

2007

tom 34

nr 2

237-252

I propose a nonlinear Bayesian methodology to estimate the latent states which are partially observed in financial market. The distinguishable character of my methodology is that the recursive Bayesian estimation can be represented by some deterministic partial differential equation (PDE) (or evolution equation in the general case) parameterized by the underlying observation path. Unlike the traditional stochastic filtering equation, this dynamical representation is continuously dependent on the underlying observation path and thus it is robust to the modeling errors. Moreover, its advantages in financial econometrics are also discussed.

Valuation and optimal design to defaultable security

63%

Huang J. , Li N.

Applicationes Mathematicae

2006

tom 33

nr 3-4

305-321

Herein, we develop a backward stochastic differential equation (BSDE) valuation of securities with default risk. Consequently, the optimal recovery problem with quasi-linear utility functions is discussed with the help of the stochastic maximum principle. Finally, two important examples: the exponential and power utility cases are studied and their business implications are considered.