Ken Siu Faculty of Business and Economics, Macquarie University A PDE Approach for Risk Measures for Derivatives With Regime Switching Wednesday 19th August 14:05-14:55pm, Eastern Avenue Lecture Theatre. In this talk, we shall discuss a partial differential equation (P.D.E.) approach to evaluate coherent risk measures for derivative securities in a Markovian regime-switching Black-Scholes-Merton environment. In such a paradigm, the dynamics of underlying risky asset are governed by a Markovian regime-switching Geometric Brownian Motion; that is, the appreciation rate and the volatility in the log-normal dynamics of the underlying risky asset switch over time according to the state of a continuous-time, finite-state, Markov chain. The states of the chain are interpreted as different states of an economy. The P.D.E. approach provides market practitioners with a flexible and effective way to evaluate risk measures in the Markovian regime-switching Black-Scholes-Merton model. We shall demonstrate the use of the P.D.E. approach for evaluating risk measures for complex options, such as American options and barrier options. Joint work with Robert J. Elliott and Leunglung Chan.