Portfolio optimization with hedging in strictly convergent coevolutionary markets

The portfolio optimization problem with hedging adapted utility function is studied within a fully computerized multi-agent market system. We clarify the conditions under which static approaches such as constraint optimization with stochastic rates or stochastic programming apply in coevolutionary markets with strictly maximal market players under scaled genetic algorithms. Convergence to global optimum is discussed for (1) coevolution of buying and selling strategies and for (2) coevolution of portfolio strategies and asset distributions over market players. Since only a finite population size in our setting suffices for the asymptotic convergence, the design criteria for genetic algorithm given (explicit cooling scheme for mutation and crossover, exponentiation schedule for fitness-selection) are of practical importance. Finally, a Java model of stationary market was developed and made available for use and download.