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In this paper, we study the problem of computing tail conditional expectations (TCE) or portfolio gains at specific times (T) in the future. We present efficient algorithms to handle the following two cases: (1) we have only one option (call or put) in our portfolio, denoted as a single-stock-single-option portfolio (SSSO); (2) we have a stock and some of its options in our portfolio, denoted as a single-stock-multiple-option portfolio (SSMO). Compared with previous simulation algorithms, our algorithms compute TCE of a given portfolio more efficiently and still maintain the same degree of accuracy. In the SSSO case, we reduce the computational time complexity from the SSSO-Naïve Algorithm's O(m*n) to SSSO algorithm's O(m+n), where m is the number of possible price outcomes for an underlying stock at time T and n is the number of possible price outcomes for an underlying stock at time U (maturity) in respect to each possible price outcome for an underlying stock at time T. In the SSMO case, we provide two algorithms to compute the TCE. The computational time complexity of the SSMO-Naive Algorithm is O(q*m*n+m*log(m)), where q is the number of options. The computational time complexities of our two algorithms are O(q*(m+n)+m*log(m)), and O(q*log(q)+n+m*q+ m*q*log(q)+m*log(m)) or O(q*log(q)+n+m*q+m*q*log(m)+m* log(m)). In both cases, our experiments show that when m and n are greater than five thousand, our algorithms run thousands of times faster than the naive algorithms. [ABSTRACT FROM AUTHOR]

The continued advancement of software-defined radio (SDR) technology has been a key factor in furthering research about the implementation of most signal processing algorithms at baseband. Traditionally, most algorithms have been carried out at radio frequency (RF). With the coming of SDR, the processing can be done at baseband frequencies which are more compatible with the fast developing software radio technology. This paper looks at matched filter detection and investigates the possibility and benefits of carrying out the detection process at quadrature baseband (QBB). A simple chirp signal is considered for the analysis. The analysis is carried out using MatLab simulations at RF and QBB and the results do show the possibility of carrying out the detection process at QBB with the expected benefits as compared to carrying out the process at RF. [ABSTRACT FROM AUTHOR]