Bose description of the generalized Pauli spin operators and para super symmetry

In this paper, the generalized fermion algebra is introduced so as to have the [Formula: see text]-dimensional Fock space. The generalized Pauli spin matrices of order [Formula: see text] are introduced by identifying these matrices with the step operators of the generalized fermion algebra. From the [Formula: see text]-graded parity relation [Formula: see text] generalized Pauli matrices are obtained. Finally, the para super symmetry (SUSY) is realized in terms of these matrices and ordinary bosonic operators.

Pricing Options and Convertible Bonds Based on an Actuarial Approach

This paper discusses the pricing problem of European options and convertible bonds using an actuarial approach. We get the pricing formula of European options, extend the pricing results to the case with continuous dividend, and then derive the call-put parity relation. Furthermore, we get the general expression of convertible bond price. Finally, we conduct a comparative analysis of numerical simulation and make an empirical analysis between the B-S model and the actuarial model using the actual data in the Chinese stock market. The empirical results show that the efficiency of the actuarial model is superior to the B-S model.