A Singular Stochastic Control Approach for Optimal Pairs Trading with Proportional Transaction Costs

Optimal trading strategies for pairs have been studied by models that try to find either optimal shares of stocks assuming no transaction costs or timing fixed numbers with costs. To determine optimally both trade times and number in a process, we use singular stochastic control approach study an problem proportional Assuming cointegrated relationship pair stock log-prices, consider portfolio optimization involves dynamic We show the value function is unique viscosity solution nonlinear quasi-variational inequality, which equivalent free boundary function. then develop discrete time programming algorithm compute regions, convergence discretization scheme. illustrate our numerical examples discuss impact different parameters on regions. out-of-sample performance empirical consists six U.S. selected from industry sectors, demonstrate efficiency strategy.