Seminar| Institute of Mathematical Sciences
Speaker: Frank Yulin Feng, Shanghai University of Finance and Economics
Abstract: The design of optimal hedging strategies is important in insurance and other financial markets. If a market is incomplete, or if an agent's initial wealth or hedging cost is constrained, then both perfect-hedging and super-hedging strategies may not exist or may be too costly. For such cases, partial-hedging strategies, which minimize exposure to a specific extent under certain risk measures, have been proposed. In the present work, we provide a unified approach to designing optimal partial-hedging strategies using range value-at-risk (RVaR), a general distortion measure introduced by Cont et al. (2010) and further developed by Embrechts et al. (2018). We prove that the non-convex optimization problem under RVaR can be transformed into a convex optimization problem under conditional value-at-risk (CVaR), and then derive semi-explicit solutions using the Neyman-Pearson lemma. We further show that optimal solutions under the value-at-risk (VaR) and CVaR measures can be derived directly as special cases of our solution. Finally, we discuss hedging applications for equity-linked insurance products, offering a generalized partial-hedging strategy under RVaR, and demonstrating that RVaR provides a bridge between VaR and CVaR.