Nonconvex optimization for pricing and hedging in imperfect markets †

The paper deals with imperfect financial markets and provides new methods to overcome many inefficiencies caused by frictions. Transaction costs are quite general and far from linear or convex. The concepts of pseudoarbitrage and efficiency are introduced and deeply analyzed by means of both scalar and vector optimization problems. Their optimality conditions and solutions yield strategies to invest and hedging portfolios, as well as bid-ask spread improvements. They also point out the role of coalitions when dealing with these markets. Several sensitivity results will permit us to show that a significant transaction costs reduction is very often feasible in practice, as well as to measure its effect on the general efficiency of the market. All these findings may be especially important for many emerging and still illiquid spot or derivative markets (electricity markets, commodity markets, markets related to weather, inflation-linked or insurance-linked derivatives, etc.).