Title:  Optimal Trading Strategies for Correlated Assets in  Regime Switching Levy Markets

Abstract: 

This paper is concerned with the optimal execution of large positions of two or multiple correlated assets when their underlying price dynamics follow Markov switching Levy processes. We particularly study the problem of simultaneously buying and selling highly correlated assets so as to maximize the overall return of these transactions. We tackle this issue using the stochastic control framework. Weprove the existence of optimal trading policies, moreover we characterize the value function as the unique viscosity solution of the associated HJB equations.We propose an approximating scheme to the value function and prove its convergence. Numerical examples are reported to illustrate the results.