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Portfolio optimization is an important process in finance that consists infinding the optimal asset allocation that maximizes expected returns whileminimizing risk. When assets are allocated in discrete units, this is acombinatorial optimization problem that can be addressed by quantum andquantum-inspired algorithms. In this work we present an integer simulatedannealing method to find optimal portfolios in the presence of discretizedconvex and non-convex cost functions. Our algorithm can deal with large sizeportfolios with hundreds of assets. We introduce a performance metric, the timeto target, based on a lower bound to the cost function obtained with thecontinuous relaxation of the combinatorial optimization problem. This metricallows us to quantify the time required to achieve a solution with a givenquality. We carry out numerical experiments and we benchmark the algorithm intwo situations: (i) Monte Carlo instances are started at random, and (ii) thealgorithm is warm-started with an initial instance close to the continuousrelaxation of the problem. We find that in the case of warm-starting withconvex cost functions, the time to target does not grow with the size of theoptimization problem, so discretized versions of convex portfolio optimizationproblems are not hard to solve using classical resources. We have applied ourmethod to the problem of re-balancing in the presence of non-convex transactioncosts, and we have found that our algorithm can efficiently minimize thoseterms.

Portfolio optimization with discrete simulated annealing