Optimal dynamic cointegrated pairs trading strategies with state-dependent risk aversion

Cointegrated pairs trading attempts to make profits when cointegrated assets depart from their equilibrium. For the mean-variance model with constant risk aversion, the optimal dynamic cointegrated pairs trading strategy shows that the allocation amounts on risky assets depend only on time but not on wealth, which goes against common sense.The optimal allocation of cointegration assets under the mean-variance model with state-dependent risk aversion was studied, and an algebraic form of the optimal strategy was obtained by solving an extended HJB equation. The strategy shows that the optimal allocation amounts depend not only on time but also on current wealth, and the strategy makes sure that the total assets remain positive all the time. Thus our strategy is more economically reasonable compared to those under constant risk aversion. The numerical example implies that our strategy behaves more steadily in terms of asset allocation, and there is an increasing trend in the allocation amounts as time goes by, a in contrast to the strategy under constant risk aversion. In addition, the influence of cointegration coefficients matrix and mean-reverting speed on the strategy was studied and explained.