Minimum cost super-hedging in a discrete time incomplete multi-asset binomial market

We consider a multi-asset incomplete model of the financial market, where each of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="m greater-than-or-equal-to 2"> <mml:semantics> <mml:mrow> <mml:mi>m</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> <mml:annotation encoding="application/x-tex">m\geq 2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> risky assets follows the binomial dynamics, and no assumptions are made on the joint distribution of the risky asset price processes. We provide explicit formulas for a non-self-financing minimum cost super-hedging strategy for a wide class of European type multi-asset contingent claims. This class includes European basket call and put options, among others. We also give explicit formulas for non-negative local residual amounts that are produced by a non-self-financing arbitrage super-hedging strategy at every time step. This paper completes the foundation started in the previous work of the authors for the extension of our results to a more realistic market model.