An extension of the Wang transform derived from Bühlmann's economic premium principle for insurance risk

It is well known that the Wang transform [Wang, S.S., 2002. A universal framework for pricing financial and insurance risks. Astin Bull. 32, 213-234] for the pricing of financial and insurance risks is derived from Bühlmann's economic premium principle [Bühlmann, H., 1980. An economic premium principle. Astin Bull. 11, 52-60]. The transform is extended to the multivariate setting by [Kijima M., 2006. A multivariate extension of equilibrium pricing transforms: The multivariate Esscher and Wang transforms for pricing financial and insurance risks, Astin Bull. 36, 269-283]. This paper further extends the results to derive a class of probability transforms that are consistent with Bühlmann's pricing formula. The class of transforms is extended to the multivariate setting by using a Gaussian copula, while the multiperiod extension is also possible within the equilibrium pricing framework.

RECENT ADVANCES IN FINANCIAL ENGINEERING 2009:

This book consists of 11 papers based on research presented at the KIER-TMU International Workshop on Financial Engineering, held in Tokyo in 2009. The Workshop, organised by Kyoto University's Institute of Economic Research (KIER) and Tokyo Metropolitan University (TMU), is the successor to the Daiwa International Workshop on Financial Engineering held from 2004 to 2008 by Professor Kijima (the Chair of this Workshop) and his colleagues. Academic researchers and industry practitioners alike have presented the latest research on financial engineering at this international venue.These papers address state-of-the-art techniques in financial engineering, and have undergone a rigorous selection process to make this book a high-quality one. This volume will be of interest to academics, practitioners, and graduate students in the field of quantitative finance and financial engineering.Financial Engineering, Mathematical Finance, Credit Risk, Real Options, Optimal Investment, Heterogeneous Beliefs