Optimal Dynamic Cointegrated Pairs Trading Strategies With State

Cointegrated pairs trading attempts to take profits when cointegrated assets depart from their equilibrium.For the mean-variance model with constant risk aversion,the optimal dynamic cointegrated pairs trading strategies show that the amounts of alloca-tion on risky assets only depend on time and not on wealth,which does not meet the common sense.In this paper,we establish a mean-variance model with state-dependent risk aversion and obtain an algebraic form of the optimal strategy by solving an ex-tended HJB equation.A numerical algorithm of the optimal strategy is also provided.The strategy shows that the optimal allocation amount depends not only on time but also on current wealth,which is more economically reasonable compared to that under constant risk aversion.The numerical example implies that there is an increasing trend in the amount and proportion of allocation as time goes by,which is in contrast to the strategies under constant risk aversion.Further,our strategy behaves steadier in terms of asset allocation and makes the total assets positive all the time while the optimal strat-egy under constant risk aversion could't ensure that.We use real data to verify these advantages.Besides,we study the influence of cointegration coefficients matrix and mean-reverting speed on the strategy and try to explain the influence.