An HJM approach to equity derivatives ”

There has been recent interest in applying the Heath-JarrowMorton interest rate framework to other areas of financial modelling. Unfortunately, there are serious technical challenges in implementing the approach for modelling the dynamics of the implied volatility surface of a given stock. By a suitable change of parametrisation, we derive an HJMstyle SPDE and discuss its existence theory. We survey some recent negative results to illustrate some of the technical challenges. Olivier Menoukeu-Pamen (University of Liverpool) “Maximum principles of Markov regime-switching forward-backward stochastic differential equations with jumps and partial information” Abstract. This paper presents three versions of maximum principle for a stochastic optimal control problem of Markov regime-switching forwardbackward stochastic differential equations with jumps (FBSDEJs). A general sufficient maximum principle for optimal control for a system driven by a Markov regime-switching forward and backward jumpdiffusion model is developed. After, an equivalent maximum principle is proved. Malliavin calculus is employed to derive a general stochastic maximum principle for non-Markovian system. The latter does not required concavity of Hamiltonian. Applications of the stochastic maximum principle to non-concave Hamiltonian and recursive utility maximization are also discussed. This paper presents three versions of maximum principle for a stochastic optimal control problem of Markov regime-switching forwardbackward stochastic differential equations with jumps (FBSDEJs). A general sufficient maximum principle for optimal control for a system driven by a Markov regime-switching forward and backward jumpdiffusion model is developed. After, an equivalent maximum principle is proved. Malliavin calculus is employed to derive a general stochastic maximum principle for non-Markovian system. The latter does not required concavity of Hamiltonian. Applications of the stochastic maximum principle to non-concave Hamiltonian and recursive utility maximization are also discussed. Albert Ferreiro-Castilla (Queen Mary University, London) “Euler-Poisson schemes for Lévy processes” Abstract: In this talk we will contextualize the recently established Wiener-Hopf Monte Carlo (WHMC) simulation technique for Levy processes from Kuznetsov et al. [4] into a more general framework allowing us to use the same technique in a larger set of problems. We will briefly show how the scheme can be used to approximate Levy driven SDEs, be enhanced with a multilevel Monte Carlo scheme, or approximate different types of path-quantities. In this talk we will contextualize the recently established Wiener-Hopf Monte Carlo (WHMC) simulation technique for Levy processes from Kuznetsov et al. [4] into a more general framework allowing us to use the same technique in a larger set of problems. We will briefly show how the scheme can be used to approximate Levy driven SDEs, be enhanced with a multilevel Monte Carlo scheme, or approximate different types of path-quantities.