Harnack inequality and no-arbitrage bounds for self-financing portfolios

Abstract

We give a direct proof of the Harnack inequality for a class of Kolmogorov operators associated with a linear SDE and we find the explicit expression of the optimal Harnack constant. We discuss some possible implication of the Harnack inequality in finance: specifically we infer no-arbitrage bounds for the value of self-financing portfolios in terms of the initial wealth.Harnack inequality; no-arbitrage principle; self-financing portfolio; Kolmogorov equation; linear stochastic equation