Application of Financial Risk-Reward Theory to Adaptive Transmission

This paper introduces a novel quantitative framework for measuring the risk and the reward provided by adaptive transmission schemes. In particular, the reward is measured as the expected value of the link spectral efficiency in excess of some predefined threshold. The risk, on the other hand, is the nth root of the nth order lower partial moment of the link spectral efficiency distribution. We apply mathematical tools of finance theory to analyze the risk-reward performance of various state-of-the-art adaptive transmission schemes in generic multi- antenna channels. We identify the maximum-return, minimum- risk, efficient, and optimal risk-reward schemes. The numerical results suggest that in a general case the optimal risk-reward scheme is neither the scheme that maximizes the expected link spectral efficiency nor the scheme that minimizes the risk by minimizing, e.g., the outage probability. The financial risk-reward theory brings a new intuition to the understanding of adaptive transmission in nonergodic channels.